1.

Write the truth values of the following :(i) 4 is odd or 1 is prime.(ii) 64 is a perfect square and 46 is a prime number.(iii) 5 is a prime number and 7 divides 94.(iv) It is not true that 5 – 3i is a real number.(v) If 3 × 5 = 8, then 3 + 5 = 15.(vi) Milk is white if and only if sky is blue.(vii) 24 is a composite number or 17 is a prime number.

Answer»

(i) Let p : 4 is odd. 

q : 1 is prime. 

Then

The symbolic form of the given statement is p∨q. 

The truth values of both p and q are F. 

∴ the truth value of p v q is F. … [F ∨ F = F]

(ii) Let p : 64 is a perfect square. 

q : 46 is a prime number. 

Then,

The symbolic form of the given statement is p∧q. 

The truth values of p and q are T and F respectively. 

∴ the truth value of p ∧ q is F. … [T ∧ F ≡ F]

(iii) Let p : 5 is a prime number.

q : 7 divides 94.

Then the symbolic form of the given statement is p∧q. 

The truth values of p and q are T and F respectively. 

∴ the truth value of p ∧ q is F. … [T ∧ F ≡ F]

(iv) Let p : 5 – 3i is a real number. 

Then,

The symbolic form of the given statement is ~ p. 

The truth values of p is F. 

∴ the truth values of ~ p is T. … [~ F ≡ T]

(v) Let p : 3 × 5 = 8. 

q : 3 + 5 = 15.

Then,

The symbolic form of the given statement is p → q.

The truth values of both p and q are F. 

∴ the truth value of p → q is T. … [F → F ≡ T]

(vi) Let p : Milk is white. 

q : Sky is blue.

Then,

The symbolic form of the given statement is p ↔ q. 

The truth values of both p and q are T. 

∴ the truth value of p ↔ q is T. … [T ↔ T ≡ T]

(vii) Let p : 24 is a composite number. 

q : 17 is a prime number.

Then,

The symbolic form of the given statement is p ∨ q. 

The truth values of both p and q are T.

∴ the truth value of p ∨ q is T. … [T ∨ T ≡ T]


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