Exercise 1.4 (2)

Find truth value of each of the following statements.

i) It is not true that 3 − 7i is a real number.
Ans:
Let p : 3 – 7i is a real number.
The Truth Value of p is F.
The given Statement in Symbolic form is ~ p.
∴ ~ p ≡ ~F ≡ T
∴ Truth value of the given statement is T.

ii) If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
Ans: 
Let p : A joint venture is a temporary partnership.
      q : Discount on purchase is credited to the supplier.
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) Every accountant is free to apply his own accounting rules if and only if machinery is an asset.
Ans: 
Let p : Every accountant is free to apply his own accounting rules
      q : Machinery is an asset.
The Truth Value of p and q are F and  T respectively.
The given Statement in Symbolic form is p ↔q.
∴ p ↔q ≡ F ↔ T ≡ F
∴ Truth value of the given statement is F.

iv) Neither 27 is a prime number nor divisible by 4.
Ans: 
Let p : 27 is a prime number
      q : 27 is divisible by 4
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 ≡ T∧T≡T
∴ Truth value of the given statement is T.

v) 3 is a prime number and an odd number.
Ans: 
Let p : 3 is a prime number
      q : 3 is an odd number.
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.