Write the component statements of the following compound statements and check whether the compound statement is true or false
· (i) Venus is the smallest and. Jupiter is the largest planet of solar system.
(ii) India is a country and Asia is a continent.
(iii) Commutative law holds for addition and subtraction of rauonal number.
(iv) Additive inverse exists for natural number and rational nutnber
(v) 32 is a multiple of 2, 3 and 4.

Explanation

(i) The component statements are p: Venus is the smallest planet of sun. (True)
q : Jupiter is the largest of sun . (True)
Both p and q are true statemerits, therefore the compound- statement is true
(ii) The component statements are
p : India is a country. (True)
q : Asia is a continent. (True)
Both p and q are true so compound statement is true
(iii) The component statements are
p : Commutative lavv holds for addition of rational numbers (True)
p : Commutative law holds for addition of rational numbers (True)
q : Commutative law holdes for subtraction of rational numbers (False)
p is true and q is false, so compound statement is false
The component statements are
p : Additive inverse exists for natural number. (False)
q : Additive inverse exists for rational number. (True)
p is false and q is true: so cornpound statement is false
The component statements are
p : 32 is 9 multiple of 2. (True)
q : 32 is a multfple of 3. (False)
r : 32 is a multiple of 4 . (True)