Again, it’s a Friday afternoon, so this is the lightning speed round of some essential 4.2 definitions that struck my fancy so I can be done !

### Contrapositive

If you have a statement *if p(x), then q(x)*,* *the contrapositive is *if ~p(x), then ~q(x).*

So, say we have the statement *if it’s friday, kate is probably crying over all the homework she has for the weekend,* the contrapositive would be *if it’s not friday, then kate is probably not crying over all the homework she has for the weekend. *

Fun fact! They logically mean the same thing.

If we have an implication statement *p(x)⇒q(x)*, the contrapositive is *~p(x)⇒~q(x). *So if we have an implication statement like *kate drinking coffee in class implies a snarky kate, *the contrapositive of this is *kate not drinking coffee in class implies a non-snarky kate. *

**Theorem 4.13:** ~[p(x) and q(x)] is logically equivalent to “~p(x) or ~q(x)”.

**Theorem 4.14:** ~[p(x) or q(x)] is logically equivalent to “~p(x) and ~q(x)”.

### Converse

If you have a statement *if p(x), then q(x)*,* *the converse is *if q(x), then p(x).*

So, say we have the statement *if it’s friday, kate is probably crying over all the homework she has for the weekend,* the converse would be *if kate is crying over all the homework she has for the weekend, then it’s friday.*

If we have an implication statement *p(x)⇒q(x)*, the converse is q*(x)⇒p(x). *So if we have an implication statement like *kate drinking coffee in class implies a snarky kate, *the converse of this is *a snarky kate implies a kate drinking coffee in class.*