Form the bi conditional statement p ↔ q,

Question:

Form the bi conditional statement p ↔ q, where

(i) p: The unit digit of an integer is zero. q: It is divisible by 5.

(ii) p: A natural number n is odd. q: Natural number n is not divisible by 2.

(iii) p: A triangle is an equilateral triangle. q: All three sides of a triangle are equal.

 

Solution:

(i) p: The unit digit of an integer is zero. q: It is divisible by 5.

In the bi conditional statement, we use if and only if.

p: The unit digit of an integer is zero.

q: It is divisible by 5.

Then,

p ↔ q = Unit digit of an integer is zero if and only if it is divisible by 5.

(ii) p: A natural number n is odd. q: Natural number n is not divisible by 2.

In the bi conditional statement, we use if and only if.

p: A natural number n is odd.

q: q : Natural number n is not divisible by 2.

Then,

p ↔ q = A natural number is odd if and only if it is not divisible by 2.

(iii) p: A triangle is an equilateral triangle. q: All three sides of a triangle are equal.

In the bi conditional statement, we use if and only if.

p: A triangle is an equilateral triangle

q: All three sides of a triangle are equal.

Then,

p ↔ q = A triangle is an equilateral triangle if and only if all three sides of triangle are equal.

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