Let p, q, and r be the propositions p : You have the flu.
q : You miss the final exam.
r : You pass the course.
Express each of these propositions as an English sentence. (a) p → q
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(b) ¬q ↔ r
(c) q → ¬r
(d) p ∨ q ∨ r
(e) (p → ¬r)∨(q → ¬r) (f) (p ∧ q) ∨ (¬q ∧ r)
1/4 CSI2101/UOttawa/MdH/S21
Let p, q, and r be the propositions
p : You get an A on fnal exam.
q : You do every exercise in the textbook.
r : You get an A in the course.
Write these propositions using p, q, and r and logical connectives (including nega- tions).
(a) You get an A in the course, but you do not do every exercise in the textbook.
(b) You get an A on fnal exam, you do every exercise in the textbook, and you get an A in the course.
(c) To get an A in the course, it is necessary for you to get an A on the final.
(d) You get an A on the final, but you do not do every exercise in the textbook; nevertheless, you get an A in the course.
(e) Getting an A on the final and doing every exercise the textbook is sufficient for getting an A in the course.
(f) You will get an A in the course if and only if you either do every exercise in the textbook or you get an A on the final.
2/4 CSI2101/UOttawa/MdH/S21
Determine whether these biconditionals are true or false. (a) 2 + 2 = 4 if and only if 1 + 1 = 2.
(b) 1 + 1 = 2 if and only if 2 + 3 = 4.
(c) 1 + 1 = 3 if and only if monkeys can fly.
(d) 0 > 1 if and only if 2 > 1
For each of these sentences, determine whether an inclusive OR, or an exclusive OR, is intended.
(a) Experience with C++ or Java required.
(b) Lunch includes soup or salad.
(c) To enter the country you need a passport or a voter registration card. (d) Publish or perish.
3/4 CSI2101/UOttawa/MdH/S21
State the converse, contrapositive, and inverse of each of these conditional state- ments.
(a) If it snows tonight, then I will stay at home.
(b) When I stay up late, it is necessary that I sleep until noon.
If p1, p2, …, pn are n propositions, explain why ∧n−1 ∧n (¬pi ∨¬pj)
i=1 j =i+1
is true if and only if at most one of p1, p2, …, pn is true.
For each of these compound propositions, use the conditional-disjunction equiva- lence to find an equivalent compound proposition that does not involve conditionals.
(a) ¬p → ¬q
(b) (p ∨ q) → ¬p
(c) (p → ¬q) → (¬p → q)
4/4 CSI2101/UOttawa/MdH/S21
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