<h2>
Answer with explanation:</h2>
Given propositions: p ="Swimming at the New Jersey shore is allowed"
q = "Sharks have been spotted near the shore"
We need to express each of these compound propositions as an English sentence.
a) ¬q : not q
Sentence: Sharks have not been spotted near the shore.
b) p ∧ q : p and q
Sentence: Swimming at the New Jersey shore is allowed and sharks have been spotted near the shore.
c) ¬p ∨ q : not p or q.
Sentence: Swimming at the New Jersey shore is not allowed or sharks have been spotted near the shore.
d) p → ¬q : If p then not q.
Sentence: If swimming at the New Jersey shore is allowed then sharks have not been spotted near the shore.
e) ¬q → p : If not q then p.
Sentence: If sharks have not been spotted near the shore then swimming at the New Jersey shore is allowed .
f) ¬p → ¬q : If not p then not q.
Sentence: If swimming at the New Jersey shore is not allowed then sharks have not been spotted near the shore.
g) p ↔ ¬q : p if and only if not q
Sentence: Swimming at the New Jersey shore is allowed if and only if sharks have not been spotted near the shore.
h) ¬p ∧ (p ∨ ¬q) : not p and, p or not q.
Sentence: Swimming at the New Jersey shore is not allowed and, swimming at the New Jersey shore is allowed or sharks have not been spotted near the shore.
