Question

For each of the following compounds statements first identify the connecting words and then break it into component statements. 

(i) All rational numbers are real and all real numbers are not complex. 

(ii) Square of an integer is positive or negative 

(iii) The sand heats up quickly in the sun and doesnot cool down fast at night. 

(iv) x = 2 and x = 3 are the roots of the equation 3x²  – x -10 = 0

Answer 1

(i) ‘and’ is the connecting word. 

∴ component statements are 

p : all rational numbers are real 

q : all real numbers are not complex. 

(ii) Connecting word is ‘or’ component statements are 

p : square of an integer is positive 

q : square of an integer is negative 

(iii) Connecting word is ‘and’ component statements are 

p : sand heats up quickly in the sun 

q : sand does not cool down fast at night 

(iv) Connecting word is ‘and’Component statements are 

p : x – 2 is a root of 3x²  – x – 10 = 0 

q : x = 3 is a root of 3x²  – x – 10 = 0