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.)
-J ≡ (∼K • L)
L ⊃ J / L ⊃ K
A) Valid
B) Invalid. Counterexample when J and L are true and K is false
C) Invalid. Counterexample when J is true and L and K are false
D) Invalid. Counterexample when L is true and J and K are false
E) Invalid. Counterexample when J, K, and L are false

Question

Quizplus · Accepted Answer

The argument is invalid because there is a situation (counterexample) where the premises are true but the conclusion is false. This occurs when J and L are true, but K is false. This is because the truth of L does not guarantee the truth of K, as shown in the given counterexample.

Construct a Complete Truth Table for Each of the Following