Question

Find the component statements of the following compound statements and check whether they are true or false. 

(i) Numbers 3 is prime or it is odd 

(ii) All integers are positive or negative 

(iii) 100 is divisible by 3,11 and 5 

(iv) A square is a quadrilateral and its four sides equal 

(v) All prime numbers are either even or odd 

(vi) Chandigarh is the capital of Haryana and P. 

(vii) 24 is a multiple of 2, 4 and 8

Answer 1

(i) The component statements are 

p : number 3 is prime 

q : number 3 is odd 

Both p and q are true 

(ii) The component statements are 

p : all integers are positive 

q : all integers are negative 

Both p and q are false 

(iii) The component statements are 

p : 100 is divisible by 3 (false) 

q : 100 is divisible by 11 (false) 

r : 100 is divisible by 5 (true) 

(iv) The component statements are 

p : a square is a quadrilateral 

q : a square has all its sides equal 

Both p and q are true 

(v) The component statements are 

p : all prime numbers are even 

q : all prime numbers are odd 

Both p and q are false 

(vi) The component statements are 

p : Chandigarh is the capital of Haryana (True) 

q : Chandigarh is the capital of U.P.(False) 

(vii) The component statements are 

p : 24 is a multiple of 2 (True) 

q : 24 is a multiple of 4 (True) 

r : 24 is a multiple of 8 (True)