Question

Let s be the proposition "I will go swimming", h the proposition "It's hot", and r the proposition "It's raining". Express the following sentences in propositional logic
a. "I will go swimming provided that it's hot and not raining"
b. "I will go swimming unless it is raining
c. "I will go swimming only if it is hot"
d. "For me to go swimming, it is necessary that it's not raining

Answer 1

Answer:

a) h∧¬r→s

b) r→¬s

c) s→h

c) s→¬r

Step-by-step explanation:

a) The sufficient condition for "I will go swimming" is "it's hot and not raining" . With your variables, the sufficient condition for s is h∧¬r. Then, if  h∧¬r is true, s will be true, which means that h∧¬r implies s.

b) This means that the only thing that would stop you from go swimming is that its raining. Then, if it rains, you won't go swimming, that is, r implies ¬s.

c) It is necessary (it must happen) that it is hot for you to go swimming. Then, it you are swimming, it must be hot (otherwise you wouldn't be swimming), hence s implies h

d) Just as in c), if you go swimming, it must not be raining. Then s implies not r.

Some final comments. Suppose you have the implication p→q. Then, it is equivalent to say:

• p is sufficient for q (If p then q)
• q is necessary for p (p only if q)