Discussion
Let a, b, c, d be propositions. Assume that the equivalence a ↔ (b v ˥b) and b ↔ c hold. Then truth value of the formula ( a ^ b) → ((a ^ c) v d) is always
Answer: A
Correct answer: True
The first equivalence makes a equivalent to \( b \lor \lnot b \), which is a tautology, so a is always true. Now suppose the antecedent \( a \land b \) holds; then b is true, and since \( b \leftrightarrow c \), c is true too, so \( a \land c \) is true and the consequent holds. The implication is therefore true in every case.
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