Answer to Question #162893 in Discrete Mathematics for wafa omer

Question

I.                   p is "x< 50"; q is "x> 40".

Express the following compound propositions as English sentences in as natural a     way as you can

 (a) ¬p

(b) ¬q

(d) p∨q

(e) ¬pV q

(f) ¬pV ¬q

Answer 1

Let $p$ is "$x< 50$ "; $q$ is "$x> 40$ ". Let us express the following compound propositions as English sentences in a natural way:

(a) $\neg p$ : "x is greater than or equal to 50"

(b) $\neg q$ : "x is less than or equal to 40"

(d) $p\lor q$ : "x is less than 50 or x is greater than 40"

(e) $\neg p\lor q$ : "x is greater than or equal to 50 or x is greater than 40" which is equivalent to "x is greater than 40"

(f) $\neg p\lor \neg q$ : "x is greater than or equal to 50 or x is less than or equal to 40"