Problem-20

Problem-20

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.

a) ¬qr

b) ¬rp

c) pqr

d) (p→¬r)∨(q→¬r)

e) (pq)∨(¬qr)

 

Solution

 

a) ¬q→r

If you do not miss the final examination, then you pass the course.

b) ¬r↔p

You do not pass the course if and only if you have the flu.

c) p∨q∨r

You have the flu, or miss the final exam, or pass the course.

d) (p→¬r)∨(q→¬r)

It is either the case that if you have the flu then you do not pass the course or the case that if you miss the final exam then you do not pass the course.

e)  (pq)∨(¬qr)

Either you have the flu and miss the final exam, or you do not miss the final exam and pass the course.

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