Discrete Math Problem Please be sure to add explanations and

Discrete Math Problem: Please be sure to add explanations and show all steps.

3. Match the following variations of an if-then statement with the following term, given that p q is the original statement. Circle any statements equivalent to p q.

q p                                              Inverse
¬p ¬q                                       Contrapositive
¬q ¬p                                         Converse

Solution

let me explain this problem with an example

let the conditional statement be : if a population consists of 50% men then 50% of the population must be women.

pq

If we exchange the position of the hypothesis and the conclusion we get a converse statement: if a population consists of 50% women then 50% of the population must be men.

qp -----------> converse

If we negate both the hypothesis and the conclusion we get a inverse statement: if a population do not consist of 50% men then the population do not consist of 50% women.

¬p ¬q

We could also negate a converse statement, this is called a contrapositive statement: if a population do not consist of 50% women then the population do not consist of 50% men.

¬q ¬p

THE CONTRAPOSITIVE IS EQUIVALENT TO THE ORIGINAL STATEMENT