Define and use predicates to write the statement Some of my

Define and use predicates to write the statement “Some of my test questions are not that hard.” in the form _____x ,such that _____ , then write the negation of the statement both symbolically and verbally.

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Solution

Answer :

Let us denote P(x) : x is my test book

Q(x) : x is hard

Then the given predicate statement can be written symbolically as follows :

(x) (P(x) ¬ Q(x) )

The negation of the above statement in symbolic form is :

¬ (x) (P(x) ¬ Q(x) ) (x) ¬(P(x) ¬ Q(x) )

                                 (x) ( ¬P(x) V Q(x) )

                                  (x) ( P(x) Q(x) )

So that verbally the negation of the given statement is :

\" All my text books are hard \"