Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
-B $ \lor $ ∼C
∼∼C / ∼B
A) Valid
B) Invalid. Counterexample when B and C are true
C) Invalid. Counterexample when B is true and C is false
D) Invalid. Counterexample when C is true and B is false
E) Invalid. Counterexample when B and C are false

Question

Quizplus · Accepted Answer

In the truth table for this argument, there is a row where B is true and C is true, but the conclusion ∼B is false. This provides a counterexample to the argument and shows that it is invalid. Therefore, the best choice is B.

Construct a Complete Truth Table for Each of the Following ∨ \lor ∨

Construct a Complete Truth Table for Each of the Following $\lor$