# Exercise 1.2 (2)

Write the truth values of following statements.

i) Earth is a planet and Moon is a star.
Ans: Let p : Earth is a planet.
q : Moon is a star.
The truth value of p and q are T and F respectively.
The given statement in Symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ F ≡ F
∴ Truth value of the given statement is F.

ii) 16 is an even number and 8 is a perfect square.
Ans: Let p : 16 is an even number.
q : 8 is a perfect square .
The truth value of p and q are T and F respectively.
The given statement in Symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ F ≡ F
∴ Truth value of the given statement is F.

iii) A quadratic equation has two distinct roots or 6 has three prime factors.
Ans: Let p : A quadratic equation has two distinct roots.
q : 6 has three prime factors.
The truth value of p and q are F and F respectively.
The given statement in Symbolic form is p ∨ q.
∴ p ∨ q ≡ F ∨ F ≡ F
∴ Truth value of the given statement is F.

iv) The Himalayas are the highest mountains but they are part of India in the North East.
Ans: Let p : The Himalayas are the highest mountains.
q : Himalayas are part of India in the North East
The truth value of p and q are T and T respectively.
The given statement in Symbolic form is p ∧ q.
∴ p ∧ q ≡ T ∧ T ≡ T
∴ Truth value of the given statement is T.