Given below are two pairs of statements. Combine these two statements using “if and only if”.
(i) p: If a rectangle is a square, then all its four sides are equal.
q: If all the four sides of a rectangle are equal, then the rectangle is a square.
(ii) p: If the sum of digits of a

Question

Given below are two pairs of statements. Combine these two statements using “if and only if”.
(i) p: If a rectangle is a square, then all its four sides are equal.
q: If all the four sides of a rectangle are equal, then the rectangle is a square.
(ii) p: If the sum of digits of a number is divisible by 3, then the number is divisible by 3.
q: If a number is divisible by 3, then the sum of its digits is divisible by 3.

Accepted Answer

When we are given an implication and its converse — "if $p$ then $q$" and "if $q$ then $p$" — together they can be combined into the single biconditional statement "$p$ if and only if $q$" ($p \Leftrightarrow q$).

(i) $p$: A rectangle is a square. $q$: All its four sides are equal.
Given "if $p$ then $q$" and "if $q$ then $p$".
Combined: "A rectangle is a square if and only if all its four sides are equal."

(ii) $p$: The sum of digits of a number is divisible by 3. $q$: The number is divisible by 3.
Given "if $p$ then $q$" and "if $q$ then $p$". …

Q.Given below are two pairs of statements. Combine these two statements using “if and only if”.

Concept understanding — If and Only If

Q.Given below are two pairs of statements. Combine these two statements using “if and only if”.

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