Converse Inverse Contrapositive and Dual Law

In this class, We discuss Converse Inverse Contra positive and Dual Law.

The reader should have prior knowledge of conditional connectives. Click Here.

Take the proposition p -> q.

q -> p is the converse to p -> q

¬p -> ¬q is the inverse to p -> q

¬q -> ¬p is the contra positive to p -> q

Example:

If it is raining, then the US team will not win.

P: It is raining

Q: The US team will not win.

The above statement is in the form of p -> q

Converse: p -> q

If the US team does not win, then it will rain.

Inverse: ¬p -> ¬q

If it is not raining, then the US team will win.

Contra Positive: ¬q -> ¬p

If the US team wins, then it is not going to rain

Duality Law:

X and X’ are dual if we obtain one another by changing ∨ to ∧, ∧ to ∨, T to F, and F to T.

Example:

Dual of (p ∧ q) ∨ T is (p ∨ q) ∧ F.