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.)
-S
∼T • U / ∼(T • U) • S
A) Valid
B) Invalid. Counterexample when T, U, and S are true
C) Invalid. Counterexample when T and S are true and U is false
D) Invalid. Counterexample when U and S are true and T is false
E) Invalid. Counterexample when S is true and T and U are false

Question

Quizplus · Accepted Answer

The argument is valid because for all possible truth values of T, U, and S, whenever the premises are true, the conclusion is also true. The conclusion negates the conjunction of T and U and then conjoins it with S, which is consistent with the premise S and the negation of T and U being true together.

Construct a Complete Truth Table for Each of the Following