Archangel Macsika
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.
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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))