Sum

Write converse, inverse and contrapositive of the following statement.

If x < y then x^{2} < y^{2} (x, y ∈ R)

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#### Solution

Let p: x < y,

q: x^{2} < y^{2}

Then the symbolic form of the given statement is p → q. **Converse:** q → p is the converse of p → q.

i.e. If x^{2} < y^{2}, then x < y. **Inverse:** ∼ p → ∼ q is the inverse of p → q.

i.e. If x `≥` y, then x^{2} `≥` y^{2}.

OR

If x `≮` y, then x^{2} `≮` y^{2}. **Contrapositive:** ∼ q → p is the contrapositive of p → q

i.e. If x^{2} `≥` y^{2}, then x `≥` y.

ORIf x

^{2}`≮` y

^{2}, then x `≮` y.

Concept: Converse, Inverse, and Contrapositive

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