Discrete Mathematics

Question

Let p and q be the propositions "Swimming at the Sariyer shore is al- lowed" and "Sharks have been spotted near the shore", respectively.

Express each of these compound propositions as an English sentence.

(a) ¬p ∨ q

(b) p ⇒ ¬q

(c) p ⇔ ¬q

Answer 1

¬ is a negation, so we simply negate the proposition

∨ is a logical disjunction, which is a "and/or"

⇒ is a conditional, usually written as "if ... then ..."

⇔ is a biconditional, which is "if and only if"

a) Swimming at the Sariyer shore is not allowed and/or sharks have been spotted near the shore.

b) If swimming at the Sariyer shore is allowed, then sharks have not been spotted near the shore.

c) Swimming at the Sariyer shore is allowed if and only if sharks have not been spotted near the shore.