Statement 3G
Given the following statement:
[A • (B ∨ C)] ∨ [∼ (A • B) ∨ ∼ (A • C)]
-Statement 3G is:
A) Valid.
B) Self-contradictory.
C) Tautologous.
D) Inconsistent.
E) Contingent.

Question

Quizplus · Accepted Answer

The statement is tautologous because it is true for all possible truth values of A, B, and C. Regardless of whether A is true or false, if either B or C is true, the first half of the statement is true. If neither B nor C is true, the second half of the statement is still true because either ∼(A • B) or ∼(A • C) must be true. Therefore, the entire statement is always true and is a tautology.

Statement 3G Given the Following Statement