David G. answered • 10/10/19

Experienced Discrete Mathematics teacher and tutor

Neither G1 nor G2 are true.

Let's use as suggested, that P(X) means that X is even and Q(X) means that X is odd,

G1 now becomes:

For all X, (X is odd or X is even) -> (For all X, X is odd) or (For all X, X is even)

The first part is true, since for all integers X, X is odd or X is even is true.

However, (For all X, X is odd) is false, and also (For all X, X is even) is false, so

[ (For all X, X is odd) OR (For all X, X is even) ] is false,

G2 now becomes:

There exists an integer X such that X is even -> For all integers X, X is even.

Again, the first part is true, since there are many even integers. However, the second part is false, since there are also many odd integers.

David G.

10/12/19

Ashley P.

Thanks for the response. But what do they tell about "obtaining the intutive meaning"? Does that mean we have to state whether the statement is either true or false or???10/12/19