Question

Write the converse, inverse and contrapositive of the statement "If a triangle is equilateral then it is equiangular".

Hint:

Remember the transformations for a statement "If p, then q":
- {Converse:} "If q, then p." (Swap)
- {Inverse:} "If not p, then not q." (Negate)
- {Contrapositive:} "If not q, then not p." (Swap and Negate)
A statement is always logically equivalent to its contrapositive.

Answer 1

Let \(p\) be the statement "a triangle is equilateral" and \(q\) be the statement "it is equiangular". The given statement is in the form \( p \to q \).
Step 1: Converse (\(q \to p\))) The converse is formed by swapping the hypothesis and the conclusion.
Statement: "If a triangle is equiangular then it is equilateral."
Step 2: Inverse (\(\sim p \to \sim q\))) The inverse is formed by negating both the hypothesis and the conclusion.
Statement: "If a triangle is not equilateral then it is not equiangular."
Step 3: Contrapositive (\(\sim q \to \sim p\))) The contrapositive is formed by negating and swapping the hypothesis and the conclusion.
Statement: "If a triangle is not equiangular then it is not equilateral."