Solution: Option (D) Come here is true. Explanation: Here to give order like 'Come here', or 'Go there' are not statements.
Solution: Option (C)6 is a natural number is true. Explanation: A statement is an assertive sentence if it is either true or false but not both. So here, the option (C) 6 is a natural number is...
Solution: Let's suppose $p$: $n^{2}$ is an even integer. $\sim p$: $n$ is not an even integer $q$: $n$ is also an even integer $\sim q$ $=$ $n$ is not an even integer. As, in the contrapositive, a...
Solution: It is given that for any real number $x$, $y$ if $x=y$ We now need to find $x^{2} = y^{2}$ Let's suppose $p$: $x=y$ in which $x$ and $y$ are real no. Squaring both the sides $x^{2} =...
Solution: Let's say that $p$ is false, as sum of an irrational no. and a rational no. is irrational. Let $\sqrt{\lambda }$ is irrational and $n$ is rational no. $\sqrt{\lambda } + n = r$...
Solution: (i) $p$: 125 is divisible by 5 and 7 Let's say, $q$: 125 is divisible by 5. $r$: 125 is divisible 7. So here, $q$ is true and $r$ is false. Hence, $q\wedge r$ is False As a result, $p$ is...
Solution: Given $n^{3}-n$ Let's suppose, $n$ is even Let $n = 2k$, in which $k$ is natural number ${{n}^{3}}-n={{(2k)}^{3}}-(2k)$ ${{n}^{3}}-n=2k(4{{k}^{2}}-1)$ Let’s say $k\left( 4{{k}^{2}}-1...
Solution: (i)The quantifiers refers to a phrase like ‘there exist’, ’for all’ and ‘for every’ etc. and these are used to make the prepositional statement. In the statement given “There exists a even...
Solution: (i)The quantifiers refers to a phrase like ‘there exist’, ’for all’ and ‘for every’ etc. and these are used to make the prepositional statement. In the statement given “For all negative...
Solution: (i) The quantifiers refers to a phrase like ‘there exist’, ’for all’ and ‘for every’ etc. and these are used to make the prepositional statement. In the statement given “For all real...
Solution: (i)The quantifiers refers to a phrase like ‘there exist’, ’for all’ and ‘for every’ etc. and these are used to make the prepositional statement. In the statement given “There exists a...
Solution: (i) It is known to us that a conditional statement is not logically equivalent to its converse. Converse: If the ratio of corresponding sides of 2 triangles are equal, then triangles are...
Solution: (i) It is known to us that a conditional statement is not logically equivalent to its converse. Converse: If the opposite angles of a quadrilateral are supplementary, then $S$ is cyclic....
Solution: (i) It is known to us that a conditional statement is not logically equivalent to its converse. Converse: If the triangle is equilateral, then all the 3 angles of the triangle are equal....
Solution: (i) It is known to us that a conditional statement is not logically equivalent to its converse. Converse: If you must visit Taj Mahal, then you go to Agra. (ii) It is known to us that a...
Solution: (i) It is known to us that a conditional statement is not logically equivalent to its converse. Converse: If the rectangle $R$ is rhombus, then it is square. (ii) It is known to us that a...
Solution: (i) It is known to us that a conditional statement is logically equivalent to its contrapositive. Contrapositive: If $x^{2}>1$ then, $x$ isn't a real number such that $0<x<1$.
Solution: (i) It is known to us that a conditional statement is logically equivalent to its contrapositive. Contrapositive: If natural number $n$ isn't divisible by 2 or 3, then $n$ isn't divisible...
Solution: (i) It is known to us that a conditional statement is logically equivalent to its contrapositive. Contrapositive: If the triangle isn't equilateral, then all the 3 sides of the triangle...
Solution: (i) It is known to us that a conditional statement is logically equivalent to its contrapositive. Contrapositive: If $x\ne 3$, then $x\ne y$ or $y\ne3$ (ii) It is known to us that a...
Solution: (i) We use if and only if, in the bi conditional statement. $p$: A triangle is an equilateral triangle $q$: All three sides of a triangle are equal. Therefore, $p\leftrightarrow q =$ A...
Solution: (i) We use if and only if, in the bi conditional statement. $p$: The unit digit of an integer is zero. $q$: It is divisible by 5. Therefore, $p\leftrightarrow q =$ Unit digit of an integer...
Solution: (i) In the form of conditional statement, expression is If $p$, then $q$ So now, In the statement $p$ and $q$ are $p$: Any number is prime, $q$: square of number is not prime. As a result,...
Solution: (i) In the form of conditional statement, expression is If $p$, then $q$ So now, In the statement $p$ and $q$ are $p$: You do not study $q$: you will fail. As a result, if you don't study,...
Solution: (i) In the form of conditional statement, expression is If $p$, then $q$ So now, In the statement $p$ and $q$ are $p$: The number is odd. $q$: The square of odd number is odd. As a result,...
Solution: (i) The given statement is compound statement then components are, $P$: $\mid{x}\mid$ is equal to $x$. $\sim p$: $\mid{x}\mid$ is not equal to $x$. $q$: $\mid{x}\mid$ is equal to $–x$....
Solution: (i) The statement given is compound statement whose components are, $P$: 35 is a prime number $\sim p$: 35 is not a prime number. $q$: 35 is a composite number $\sim q$: 35 is not a...
Solution: (i) The sentence given is a compound statement whose components are $p$: $x = 2$ is a root of the Quadratic equation $x^{2}{-}5x + 6 = 0$. $\sim p$: $x = 2$ is not a root of the Quadratic...
Solution: (i) The statement given is compound statement whose components are, $P$: All rational numbers are real. $\sim p$: All rational numbers are not real. $q$: All rational numbers are complex....
Solution: (i) The sentence given is a compound statement whose components are $p$: Hindi is the optional paper $q$: English is the optional paper It can now be represented in symbolic function as,...
Solution: (i) The sentence given is a compound statement whose components are $p$: A number is divisible by 2 $q$: A number is divisible by 3 It can now be represented in symbolic function as,...
Solution: (i) The sentence given is a compound statement whose components are $p$: 2 is a factor of 12 $q$: 3 is a factor of 12 $r$: 6 is a factor of 12 It can can be represented in symbolic...
Solution: (i) The sentence given here is a compound statement whose components are $p$: Rahul passed in Hindi $q$: Rahul passed in English It can now be represented in symbolic function as, $p\wedge...
(i) "Not p" is the negation of the assertion p. The negation of p is represented by $\sim p$. The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement is...
(i) "Not p" is the negation of the assertion p. The negation of p is represented by $\sim p$. The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement is...
(i) "Not p" is the negation of the assertion p. The negation of p is represented by $\sim p$. The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement is “2...
(i) "Not p" is the negation of the assertion p. The negation of p is represented by $\sim p$. The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement is...
(i) "Not p" is the negation of the statement p. The negation of p is represented by the "$\sim p$." The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement...
(i) A compound statement is made up of two or more statements (Components). As a result, the elements of the given sentence "All living things have two eyes and two legs" are as follows: p: All...
(i) A compound statement is made up of two or more statements (Components). As a result, the elements of the provided statement "57 is divisible by 2 or 3" are as follows: p: 57 is divisible by 2....
A compound statement is made up of two or more statements (Components). As a result, the elements of the given statement "A rectangle is a quadrilateral or a 5-sided polygon" are as follows: p: A...
(i) A compound statement is made up of two or more statements (Components). As a result, the parts of the supplied statement "Plants use sunshine, water, and carbon dioxide for photosynthesis" are...
(i) A compound statement is made up of two or more statements (Components). As a result, the components of the given statement 7are a rational or irrational number, respectively. p: √7is a rational...
(i) A compound statement is made up of two or more statements (Components). As a result, the components of the provided statement "The number 100 is divisible by 3, 11, and 5" are as follows. p: 100...
(i) A compound statement is made up of two or more statements (Components). As a result, the elements of the provided statement "Number 7 is prime and odd" are as follows: p: The number 7 is prime....
(i) If a statement is true or false but not both, it is a declarative sentence. "The sum of opposite angles of a cyclic quadrilateral is 180°," according to quadrilateral characteristics. As a...
(i) If a statement is true or false but not both, it is a declarative sentence. "Where is your bag?" is a question in this context. As a result, it is not a statement. (ii) Every square is a...
(i) If a statement is true or false but not both, it is a declarative sentence. As a result, the expression "15 + 8 > 23" is incorrect. Because the L.H.S result will always equal the R.H.S...
(i) If a statement is true or false but not both, it is a declarative sentence. The sentence "sky is red" is incorrect. As a result, the statement is false. (ii) If a statement is true or false but...
(i) A statement is a declarative sentence if it is either true or false but not both. Hence, it is a true statement (ii) If a statement is true or false but not both, it is a declarative sentence....
Five different ways to write the above given statement are: (I) A triangle is equiangular shows that it is an obtuse angled triangle . (ii) A triangle is equiangular provided that the triangle is a...
(I) The given assertion is as per the following p: The amount of a silly number and a judicious number is silly. Allow us to expect that the assertion \[p\] is bogus. That is, The amount of a...
The compound assertion with \['And'\] is as per the following \[25\]is a various of \[5\text{ }and\text{ }8\] This is bogus articulation since \[25\] is definitely not a numerous of \[8\] The...
A quadrilateral is equiangular if by some stroke of good luck in case it is a square shape.
(I) You stare at the TV if and provided that your brain is free (ii) You get A grade if and provided that you do all the schoolwork consistently
The assertion\[~r\] in the structure 'assuming' is as per the following Assuming you can get to the site, you pay a membership charge.
(I) The assertion p in the structure 'on the off chance that' is as per the following Assuming you sign on to the worker, you have a secret word. (ii) The assertion \[q\]in the structure 'assuming'...
The opposite of proclamation r is given underneath On the off chance that you feel parched, it is hot outside. The contrapositive of proclamation r is given underneath On the off chance that you...
(I) Statement \[p\]can be written in the structure 'assuming' is as per the following Assuming a positive number is prime, it has no divisors other than \[1\] and itself The opposite of the...
Solution:- (I) The nullification of articulation \[r\] is given underneath There exists a genuine number \[~x\], to such an extent that neither \[x\text{ }>\text{ }1\text{ }nor\text{ }x\text{...
(I) The nullification of explanation \[p\]is given beneath There exists a positive genuine number\[x\], to such an extent that \[x\text{ }\text{ }1\]isn't positive (ii) The invalidation of...
\[11\] is an indivisible number We realize that, the square base of any indivisible number is an unreasonable number. In this way \[\surd 11\] is a silly number Henceforth, the given assertion...
(i) The condition of an elipse is, In the event that we put\[~a\text{ }=\text{ }b\text{ }=\text{ }1\], we get \[{{x}^{2}}~+\text{ }{{y}^{2}}~=\text{ }1,~\], which is a condition of a circle Thus,...
(I) The given assertion \[p\]is bogus. By the meaning of harmony, it ought to meet the circle at two particular focuses (ii) The given assertion \[q\]is bogus. The middle won't cut up that harmony...
(I) Let \[q:\]All the points of a triangle are equivalent \[r:\]The triangle is an insensitive calculated triangle The given assertion \[p\]must be refuted. To show this, required points of a...
Let \[p:\]If \[x\]is a number and \[{{x}^{2}}\]is even, then, at that point, \[x\]is likewise even Let \[q:\text{ }x\]is a number and \[~{{x}^{2}}~\]is even \[r:\text{ }x\]is even By contrapositive...
The given assertion can be written as 'assuming' is given beneath Assuming \[a\text{ }and\text{ }b\]are genuine numbers to such an extent that \[{{a}^{2}}~=\text{ }{{b}^{2}},\text{ }a\text{...
Let \[p:\]'In case \[x\]is a genuine number to such an extent that \[{{x}^{3}}\text{ }+\text{ }4x\text{ }=\text{ }0,\]then, at that point, \[x\text{ }is\text{ }0'\] \[q:\text{ }x\]is a genuine...
Let \[p:\]'In case \[x\]is a genuine number to such an extent that \[{{x}^{3}}\text{ }+\text{ }4x\text{ }=\text{ }0,\]then, at that point, \[x\text{ }is\text{ }0'\] \[q:\text{ }x\]is a genuine...
(a) If a quadrilateral is a parallelogram, then, at that point, its diagonals divide one another. (I) If the diagonals of a quadrilateral don't divide one another, then, at that point, the...
(a) If you live in Delhi, then, at that point, you have winter garments. (I) If you don't have winter garments, then, at that point, you don't live in Delhi [Contrapositive of articulation (a)] (ii)...
(i) If the diagonals of a quadrilateral divide one another, then, at that point, it is a parallelogram. (ii) If you need to score an \[A+\]in the class, then, at that point, you do every one of the...
(I) If you find a new line of work, then, at that point, your qualifications are acceptable. (ii) If the Banana trees remains warm for a month, then, at that point, the trees will sprout.
The given assertion can be composed as though\[~'x\]is a significantly number, then, at that point,\[~x\] is separable by \[4'.\] The contrapositive of the given assertion is as per the following On...
(i) The contrapositive of the given assertion is as per the following On the off chance that something doesn't have low temperature, it isn't cold. The opposite of the given assertion is as per the...
(I) The contrapositive of the given assertion is as per the following Assuming a number \[x\]isn't odd, \[x\]is certifiably not an indivisible number. The opposite of the given assertion is as per...
The five unique methods of the given assertion can be composed as follows (I) A characteristic number is odd shows that its square is odd. (ii) A characteristic number is odd provided that its...
Since all numbers can't be both positive and negative. Thus, the 'or' in the given assertion is selective.
(I) It isn't workable for the Sun to rise and the Moon to set together. Thus, the 'or' in the given assertion is selective. (ii) Since an individual can have both a proportion card and a visa to...
The negative of \[\left( I \right)\] is given below There exists genuine number \[x\text{ }and\text{ }y\]for which \[x\text{ }+\text{ }y\text{ }\ne \text{ }y\text{ }+\text{ }x\] Now, this statement...
Here, the quantifier is 'there exists'. The invalidation of this assertion is as per the following In India there exists a state, which doesn't have a capital.
(I) Here, the quantifier is 'there exists'. The invalidation of this assertion is as per the following There doesn't exists a number which is equivalent to its square (ii) Here, the quantifier is...
(i) In this sentence 'and' is the associating word The part proclamations are as per the following (a) The sand warms up rapidly in the Sun (b) The sand doesn't chill off quick around evening time...
The part explanations are (a) \[100\]is detachable by \[3\] (b) \[100\]is detachable by \[11\] (c) \[100\]is separable by \[5\] Here, the articulations \[\left( a \right)\text{ }and\text{ }\left( b...
(I) The part proclamations are (a) Number \[3\] is prime (b) Number \[3\] is odd Here, both the statement are valid (ii) The part explanations are (a) All numbers are positive (b) All numbers...
(I) The invalidation of the principal proclamation is 'the number\[~x\] is a levelheaded number'. This is same as the second assertion since, in such a case that a number is certainly not a silly...
Every natural number isn't a number
(i) All triangles are symmetrical triangles (ii) The number \[2\] isn't more prominent than \[7\]
(I) Chennai isn't the capital of Tamil Nadu (ii) $\sqrt{2}$ is a complex number
The three instances of sentences, which are not articulations are given beneath: (I) He is a specialist In the given sentence, it isn't apparent concerning whom 'he' is alluded to. Hence, it is not...
(I) The given sentence isn't an assertion in light of the fact that the day that is being alluded to isn't clear from the sentence (ii) The given sentence is consistently right since all genuine...
(I) The given sentence is incorrect in light of the fact that the result of \[\left( -\text{ }1 \right)\text{ }and\text{ }8\text{ }is\text{ }\text{ }8.\]Subsequently, it is an statement (ii) The...
(I) This sentence can be once in a while right and here and there mistaken. For instance, square and rhombus have sides of equivalent lengths while trapezium and square shape have sides of...
(I) The amount of \[5\text{ }and\text{ }7\]is \[12\] and it is more prominent than \[10.\]Subsequently this sentence is consistently right. Subsequently, it is an statement (ii) This sentence can be...
(I) The greatest number of days in a month is \[31,\]so this sentence is incorrect. Subsequently it is an statement . (ii) This sentence is emotional. For certain individuals, Mathematics can be...