Test: Implications And Validating Of Statements - JEE MCQ

A quadrilateral is a rectangle if and only if its all sides are equal.

A quadrilateral is a rectangle if and only if its opposite sides are equal.

A quadrilateral is a square if and only if its opposite sides are equal.

A quadrilateral is not a rectangle if and only if its opposite sides are equal.

~ q ⇒ ~ p

~ q ⇒ p

q ⇒ p

q ⇒ ~ p

Counter example

Direct method

By Contradiction

Contrapositive method

The statement p is true and the statement q is not true

The statement p is false and the statement q is true.

The statement p is true and the statement q is false

The statement p is true and the statement q is true

By assuming that p is true, prove that q must be true.

By assuming that p is true, prove that q must be false.

By assuming that p is false, prove that q must be true

none

If p is false, then q is false.

If p is true, then q is false

If p is false, then q is true

If p is true, then q is true

You are not wet when you are in river or it rains.

You are wet when you are in river and it rains.

You are wet when it rains and you are in a river

You are wet when it rains or you are in a river.

~p implies q.

p is a sufficient condition for q.

~q implies ~p

p only if q.

Counter example

Contrapositive method

Direct method

By Contradiction