Question

Let p, q, and r be the following propositions:

The water is warm.
People are swimming.
The waves are not big.
Express each of the following sentences using p, q, r, and logical connectives: and, or, not.
A) The water is warm and people are swimming.
B) If people are not swimming, then the water is not warm or the waves are big.
C) If the waves are big and the water is warm, then the people are not swimming.

Answer 1

Answer and Step-by-step explanation:

P= the water is warm.

q = people are swimming.

r = the waves are not big.

Logical connectives are:

Not p = ¬p

P or q = p ∨ q

P and q = p ∧ q

If p, then q = p → q

P if and only if

q = p ↔ q

By using p, q, r and logic connectives and or not, we have:

1-water is warm and people are swimming.

= p ∧ q

2- If people are not swimming then water is not warm or waves are big.

= ¬q → ¬p v ¬r

3- if waves are big, water is warm then people are not swimming

= ¬r ∧ p → ¬q