Compound Statement Truth Table Idea – UGC NET Question

A statement that is always true under every possible assignment of truth values to its components is called a tautology. The disjunction “p or not p” covers all possibilities: if p is true, the first part is true; if p is false, not p is true. Thus, in all cases the compound statement evaluates to true. This makes “p or not p” a classic example of a tautology.

Option A:
Option A, “p and not p,” is instead a contradiction because it asserts that p is both true and false simultaneously. There is no assignment of truth values that can make both p and not p true together, so this statement is never true.

Option B:
Option B, “p or not p,” correctly spans all truth possibilities for p. Since one of p or not p must be true, their disjunction is always true, demonstrating tautological status.

Option C:
Option C, “p → not p,” is not always true. If p is true, the implication would require not p to be true as well, which is impossible, so the statement can be false.

Option D:
Option D, “not p → p,” also fails to be always true; there are assignments where it becomes false, so it is not a tautology.