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Let $F$ and $G$ be two propositional formula.

Which of the following is/are True?

  1. $F \vee G$ is a tautology iff at least one of them is a tautology
  2. If $F \rightarrow G$ is a tautology and $F$ is a tautology, then $G$ is a tautology.
  3. $(F \rightarrow G) \vee (F \rightarrow \neg G)$ is a tautology.
  4. $(F \rightarrow G) \wedge (F \rightarrow \neg G)$ is a tautology iff $F$ is a contradiction.
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here answer should be ABCD but given is BCD

A because FVQ so if atleast one of them is true then output is true ..
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