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Which of the following is/are tautology?

  • A.a v b → b ^ c
  • B.a ^ b → b v c
  • C.a v b → (b → c)
  • D.None of these

Answer: B

Correct answer: a ^ b → b v c

If the antecedent \( a \land b \) is true then b is true, so \( b \lor c \) is true and the implication holds; if the antecedent is false the implication holds vacuously. The other two fail: the first when a is true and b false, and the third when a is false, b true and c false.

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