Question

Negation of “ $\Delta ABC$ is an equilateral triangle if and only if it is equiangular” has a compound statement as
A) $\Delta ABC$ is equilateral and it is not equiangular
B) $\Delta ABC$ is not equilateral and it is not equiangular
C) $\Delta ABC$ is equilateral and equiangular
D) $\Delta ABC$ is either equilateral or equiangular

Answer 1

Firstly, convert the given statement into compound statements using a suitable compound word. Then, convert the compound statement into its negation.

Complete step by step solution:
It is asked to find the compound statement of negation of “ $\Delta ABC$ is an equilateral triangle if and only if it is equiangular”.
Now, converting the given statement into a compound sentence as “ $\Delta ABC$ is equilateral and equiangular”.
Now that we have the compound statement of the given sentence, we will convert it into its negation.
The negation of the compound statement can be written as “ $\Delta ABC$ is not an equilateral triangle and it is not equiangular”.

So, option (B) is the correct answer.

Note:
Compound statement:
A compound statement is a sentence that consists of two or more sentences that are separated by logical connectors.
Negation of a statement:
The statement created using ‘not’ and other similar words is called a negation of a statement. For example, “If p, then q” can be negated as “If not p, then not q”.