Answer: Argument Used: x2 = π2 is irrational So, x = π is irrational. p: “If x2 is irrational, then x is rational.” Consider, An irrational number given by x = √k  [k is a rational number] Squaring...

Answer: t: √11 is a rational number. Square root of prime numbers is irrational numbers. The statement is False.

Answers: (i) r: Circle is a particular case of an ellipse. A circle can be an ellipse in a particular case when the circle has equal axes. The statement is true. (ii) s: If x and y are integers such...

Answers: (i) p: Each radius of a circle is a chord of the circle. The Radius of the circle is not it chord. The statement is False. (ii) q: The centre of a circle bisect each chord of the circle. A...

Answer: Consider, A triangle ABC with all angles equal. [Each angle of the triangle is equal to 60] ABC is not an obtuse angle triangle. The statement “p: If all the angles of a triangle are equal,...

Answer: Consider, p: Integer n is even q: If n2 is even Let p be true. Let n = 2k Squaring both the sides, n2 = 4k2 n2 = 2.2k2 n2 is an even number. q is true when p is true. The statement is...

Answer: Consider, q: x is an integer and x2 is odd. r: x is an odd integer. p: if q, then r. Let r be false. x is not an odd integer, then x is an even integer x = (2n) for some integer n x2 = 4n2...

Answer: Method of Contradiction: If possible, let p be false. P is not true -p is true -p (p => r) is true q and –r is true x is a real number such that x3+x = 0and x≠ 0 x =0 and x≠0 This is a...

Answers: (i) Direct Method: Consider, q: x is a real number such that x3 + x=0. r: x is 0. If q, then r. Let q be true. Then, x is a real number such that x3 + x = 0 x is a real number such that...

Answers: (i) p: If x and y are odd integers, then x + y is an even integer. Conisder, p: x and y are odd integers. q: x + y is an even integer If p, then q. Let p be true. [x and y are odd integers]...

Answer: r: 60 is a multiple of 3 or 5. We know that 60 is a multiple of 3 as well as 5. Hence, the statement is true.

Answers: (i) p: 100 is a multiple of 4 and 5. We know that 100 is a multiple of 4 as well as 5. Hence, the statement is true. (ii) q: 125 is a multiple of 5 and 7 We know that 125 is a multiple of 5...