Split each of the following into simple sentences and determine whether it is true or false. (i) A line is straight and extends indefinitely in both the directions. (ii) A point occupies a position, and its location can be determined.

Split each of the following into simple sentences and determine whether it is true or false.
(i) A line is straight and extends indefinitely in both the directions.
(ii) A point occupies a position, and its location can be determined.

RS Agarwal Maths Class 11 Mathematical Reasoning

Split each of the following into simple sentences and determine whether it is true or false.
(i) A line is straight and extends indefinitely in both the directions.
(ii) A point occupies a position, and its location can be determined.

(i) p: A line is straight.
q: A line extends indefinitely in both the directions.
Both the simple sentences are TRUE; therefore, the given sentence is TRUE.

(ii) p: A point occupies a position.
q: Its location can be determined.
Both the simple sentences are TRUE; therefore, the given sentence is TRUE.

i

By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.

Use contradiction method to prove that :

By giving a counter-example, show that the statement is false :
p : If n is an odd positive integer, then n is prime.

Consider the statement :
q : For any real numbers a and b, a2 = b2⇒ a = b
By giving a counter-example, prove that q is false.

Let p : If x is an integer and x2 is even, then x is even, Using the method of contrapositive, prove that p is true.

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