Question

Write converse, inverse and contrapositive of the following statement.

If x < y then x² < y² (x, y ∈ R)

Write the inverse and contrapositive of the following statement:

If x < y then x² < y²

Answer 1

Let p: x < y,
      q: x² < y²

Then the symbolic form of the given statement is p → q.

Its converse is q → p.

If x² < y², then x < y.

Its inverse is ∼p → ∼q.

If x `≥` y, then x² `≥` y².

OR

If x `≮` y, then x² `≮` y².

Its contrapositive is ∼q → ∼p.

If x² `≥` y², then x `≥` y.
OR
If x² `≮` y², then x `≮` y.