Question

Write converse, inverse and contrapositive of :

If x < y then x² < y² (x, y ∈ R)

Answer 1

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.