Doubt in the answer for a Predicate logic question for the zoo example

Question

Form a sentence using the variables p, q, and r to denote that ”I will go to the zoo if it is sunny and I wear sunglasses”.

Let p be ”It is sunny”.

Let q be ”I wear sunglasses”.

Let r be ”I will go to the zoo”.

Is the solution to this: (r→p)∧q or r→(p∧q)

or both my suggested solutions wrong.

Answer 1

Both of your suggested solutions are incorrect.

 ”I will go to the zoo if it is sunny and I wear sunglasses”

translates to $p \wedge q \implies r$

Notice the English statement suggests that you are to go to the zoo if it is sunny and you wear sunglasses. So, the p and q must be the hypothesis of the conditional statement with r being the conclusion.

Consider these similar cases

• "I will go to the zoo if it is sunny" translates to $p \implies r$

• "I will go to the zoo if it is sunny and I wear sunglasses" translates to $p \wedge q \implies r$

• "I will go to the zoo if it is sunny and I wear sunglasses and it is Saturday" translates to $p \wedge q \wedge s \implies r$