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.