Question

Determine whether the following compound statements are true or false :

(i) Delhi is in India and 2 + 2 = 4

(ii) Delhi is in England and 2 + 2 = 4.

(iii) Delhi is in India and 2 + 2 = 5.

(iv) Delhi is in England and 2 + 2 = 5.

Answer 1

The component statements of the compound statement

Delhi is in India and 2 + 2 = 4.

are

p : Delhi is in India

q = 2 + 2= 4

We know that if a and q are true then p or q must also be true.

Hence, the compound statement is true.

(ii) The component statements of the compound statement

Delhi is in England and 2 + 2 = 4.

are

p : Delhi is in England

q = 2 + 2= 4

Here p is false and q is true. So, p and q must be false.

Hence, the compound statement is false.

(iii) The component statements of the compound statement

Delhi is in India and 2 + 2 = 5.

are

p : Delhi is in India

q : 2 + 2= 5

Here p is true and q is true. So, p and q must be false.

Hence, the compound statement is false.

(iv) The component statements of the compound statement

Delhi is in England and 2 + 2 = 5

are

p : Delhi is in England

q = 2 +2 = 5

We know that if p and q are false then p and q must also be false.

Hence, the compound statement is false.