Valid Equivalence Argument Forms

Question 1

Distribution

[P(Q v R)] = [(PQ) v (PR)]
[P v (QR)] = [(PvQ)*(PvR)]

Answer 1

If and only if p or q and r then p or q and p or q

Veg or apple and ban, veg or apple or veggies and banana

Question 2

Commutation

Answer 2

If and only if p and q then q and p

If and only if I have apples and oranges then I have oranges and apples

Question 3

Tautology

Answer 3

If an only if then p or p
If and only if p then p and p

If and only if I have apples then I have apples or apples

Question 4

Association

Answer 4

If and only p and g and t then p and q and r

You can have ice cream and you have to have meat and veggies

Question 5

Contraposition

Answer 5

If and only if if p then q, if no q then not p

If you’re a royals fan, then you have good taste

If it’s raining then I’ll have an umbrella, if it’s not raining then u ain’t have an umberella

Question 6

Exportation

Answer 6

If and only if if p and w are then if o then if q then r

If I pass my 400 lvl class and my PE course then I’ll get my gonzaga degree

Question 7

Equivalence

Answer 7

If and only if if p then q

If and only if you’re a gonzaga student then your a genius

If and only if if and only if p and q then p and q or not P and not q

If and only if gonzaga doesn’t make the tournament then I’ll be unhappy or it will not be the case

Question 8

Distribution

Answer 8

If and only if p or q and r then p or wand p or q

Veg or apple and banana, veggies or apple or veggies and banana

Veggies and either an apple or banana

Question 9

Implication

Answer 9

If and only if p then q not p or q

Either a tiger drinking orange juice or there isn’t

Question 10

Demorgans theorem

Answer 10

If and only if not p and w then not p or not q

I don’t want you to give me candy and lollipops but I will give yo candy or just lollipops