- (11) Let p and q be the propositions “Swimming at the New Jersey shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence.
- d) p → ¬q
- e) ¬q → p
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(15) Let p and q be the propositions p: You drive over 65 miles per hour. q: You get a speeding ticket. Write these propositions using p and q and logical connectives (including negations).- d) If you do not drive over 65 miles per hour, then you will not get a speeding ticket.
- e) Driving over 65 miles per hour is sufficient for getting a speeding ticket.
- f) You get a speeding ticket, but you do not drive over 65 miles per hour.
- (33) Construct a truth table for each of these compound propositions.
- f) (p → q) → (q → p)
- (12) Show that each of these conditional statements is a tautology by using truth tables.
- b) [(p → q) ∧ (q → r)] → (p → r)
- c) [p ∧ (p → q)] → q
- (26) Show that (p → q) ∧ (p → r) and p → (q ∧ r) are logically equivalent.
- (27) Show that (p → r) ∧ (q → r) and (p ∨ q) → r are logically equivalent
With and with out the truth table for 1.3.