Question

Which of the following statements is true after finding the component statements for each of the statement?

• A. A square is a quadrilateral and its four sides are equal
• B. All prime numbers are either even or odd
• C. A person who has studied in Delhi or Mumbai can go in army
• D. Chandigarh is the capital of M.P. and U.P.

Answer 1

Answer: (A)

(a) The component statements are
$p:$ A square is a quadrilateral.
$q:$ A square has all its sides equal.
We know that both these statements are true. The connecting word is and'. So, the given statement is true,
(b) The component statements are
$p:$ All prime numbers are even numbers.
$q:$ All prime numbers are odd numbers.
The connecling word is 'or'. Both these statements are false. So, the given statement is false,
(c) The component statements are
$p:$ A person who has studied in Delhi can go in army.
$q:$ A person who has studied in Mumbai can go in army.
The connecting word is or'. Both these statements are false. So, the given statement is false.
(d) The component statements are
$p:$ Chandigarh is the capital of M.P.
$q:$ Chandigarh is the capital of U.P.
The connecting word is 'and'. Both the statements are false. So, the given statement is false.