Write converse, inverse and contrapositive of :If x < y then x2 < y2 (

1.	Write converse, inverse and contrapositive of :If x < y then x2 < y2 (x, y ∈ R)
Answer» Let p : x < y, q : x < y . 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 x ≮ y , then x ≮ y.

Write converse, inverse and contrapositive of :If x < y then x2 < y2 (x, y ∈ R)

Answer»

Let p : x < y,

q : x < y .

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.

If x ≮ y, then x²≮ y².

Contrapositive : ~q → p is the contrapositive of p → q

i.e. If x² ≯ y², then x ≯ y.

If x ≮ y , then x ≮ y.