use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
-(H ⊃ ∼I) • ∼J
∼I ⊃ [(J $ \lor $ K) • (J $ \lor $ H)]
∼H $ \lor $ (K ⊃ L) / L ⊃ ∼H
A) Valid
B) Invalid. Counterexample when H, I, K, and L are true and I is false
C) Invalid. Counterexample when H, I, and L are true and J and K are false
D) Invalid. Counterexample when H, K, and L are true and I and J are false
E) Invalid. Counterexample when H, J, and L are true and I and K are false

Question

Quizplus · Accepted Answer

An indirect truth table can be used to test the validity of the argument by assuming the conclusion is false and then checking if this assumption leads to a contradiction with the premises. The counterexample provided in option D (H, K, and L are true and I and J are false) makes the premises true while the conclusion is false, indicating the argument is invalid.

Use Indirect Truth Tables to Determine Whether Each of the Following