Contrapositive of P implies Q

pimpliesqcontrapositive

Converse: Q => P

The converse of P=>Q  is Q=>P

The Premise(P) and the Conclusion(Q) switch places. The Conclusion becomes the Premise, the Premise becomes the Conclusion.

Inverse: not P => not Q

The inverse of P=>Q  is (not P => not Q)
Negate both the Premise(P) and the Conclusion(Q)

Contrapositive: not Q => not P

The Contrapositive of P=>Q  is (not Q => not P)
Contrapositive a combination of the converse and the inverse. To get the Contrapositive just Negate and switch The Premise(P) and The Conclusion(Q).

Example

P = The Traffic Light is Green

Q = The Car Drives over the crossing

P => Q is then:

If the I fall into the lake, then I get wet.

The Contratpositive of P => Q is then: not Q => not P is then:

If I am not wet, then I did not fall into the lake.

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1 Comment

  1. Pingback: Logical Identities « Jasoninclass's Blog

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