Answer to Question #251783 in Discrete Mathematics for russel

Question

Let p, q, and r be the propositions

p : You have Covid.

q : You miss the prelim examination.

r : You pass the course.

Express each of these propositions as an English sentence.

a) p → q b) ¬q ↔ r

c) q → ¬r d) p ∨ q ∨ r

e) (p → ¬r) ∨ (q → ¬r)

f ) (p ∧ q) ∨ (¬q ∧ r)

Answer 1

QUESTION

Let p, q, and r be the propositions

p : You have Covid.

q : You miss the prelim examination.

r : You pass the course.

Express each of these propositions as an English sentence.

a) p → q b) ¬q ↔ r

c) q → ¬r d) p ∨ q ∨ r

e) (p → ¬r) ∨ (q → ¬r)

f ) (p ∧ q) ∨ (¬q ∧ r)

SOLUTION

p: You have Covid.

q: You miss the prelim examination.

r: You pass the course.

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

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

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

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

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

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