Answer to Question #166370 in Discrete Mathematics for faiz

Question

Use a short truth table to determine whether or not the following argument is valid.

E -> J

B -> Q

D -> (J & ~Q)

Thus, (E & B) -> D

Question 2 options:

Valid

Invalid, with J is false, Q is true.

Invalid, with D is true, B is false.

Invalid, with D is false, B is true.

Invalid, with E is false, Q is true.

Answer 1

Argument is not valid if:

D is false, (E & B) is true, E -> J is true, B -> Q is true, D -> (J & ~Q) is true

So, argument is not valid, because the premises are all true and conclusion is false for:

D is false, E is true, B is true, J is true, Q is true