Answer to Question #166199 in Discrete Mathematics for Syed Hassan Ali

Question

Let p, q, and r be the propositions

p: You have the flu. q: You miss the final examination. r: You pass the course.

Express each of these propositions as an English sentence.

Answer 1

p: You have the flu.

q: You miss the final examination.

r: You pass the course.

a) p → q : If you have flu then you will miss the final examination.(Implication statement)

b) ¬q ↔ r:  You won't miss the final examination if and only if you pass the course.(Bi-conditional statement)

c) q → ¬r: If you miss the examination then you will be failing the course.(Implication Statement)

d) p ∨ q ∨ r: You have the flu OR you miss the final examination OR you pass the course.(Disjunction Proposition)

e) (p → ¬r) ∨ (q → ¬r): If you have the flu then you'll not pass the course OR If you miss the final examination then you'll fail the course.((P implies not R) OR (Q implies not R))

f ) (p ∧ q) ∨ (¬q ∧ r): You have the flu and you miss the examination OR You will not miss the final examination and you pass the course.((P and Q) OR (not Q and R))