# Write converse, inverse and contrapositive of the following statement. If x < y then x2 < y2 (x, y ∈ R) - Mathematics and Statistics

Sum

Write converse, inverse and contrapositive of the following statement.

If x < y then x2 < y2 (x, y ∈ R)

#### Solution

Let p: x < y,
q: x2 < y2
Then the symbolic form of the given statement is p → q.
Converse: q → p is the converse of p → q.
i.e. If x2 < y2, then x < y.
Inverse: ∼ p  → ∼ q is the inverse of p → q.
i.e. If x ≥ y, then x2 ≥ y2.
OR
If x ≮ y, then x2 ≮ y2.
Contrapositive: ∼ q → p is the contrapositive of p → q
i.e. If x2 ≥ y2, then x ≥ y.
OR
If x2 ≮ y2, then x ≮ y.

Concept: Converse, Inverse, and Contrapositive
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