Specialist Mathematics- Proofs

Direct proof

If A implies B, assume A is true and use it to prove B is true.

De Morgan’s law

Not (P and Q) is the same as Not P or Not Q.

Not (P or Q) is the same as Not P and Not Q

Proof By contrapositive

Switching the hypothesis and conclusion and negating both.

Proof by contradiction

Start with a statement you want to prive is false, and prove that it is impossible.

Using Converse of a statement

Find it by switching the hypothesis and conclusion

Equivalent statements

If and only jfm prove the hypothesis leads to conclusion and vice versa

Proof by induction

Prove it is true for K, and K+1