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Which of the following is(are) not logical implications?

  1. p<->q => p->q
  2. p^q => p<->q
  3. p<-> => p->~q
  4. p<->~q => p->q
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The Best way to check whether $A \rightarrow B$ is a valid implication or Not, Just Try to make $A$ true and $B$ false... If you can somehow do it then it means Invalid implication. And If you can't make $A$ true and $B$ false simultaneously then Valid implication.  It's because, we know $A \rightarrow B$ is False If and Only if $A$ is True and $B$ is False.

 

1. $(P \Leftrightarrow Q) \rightarrow (P \rightarrow Q)$  Is Valid implication i.e is Tautology.

2. $(P \wedge Q) \rightarrow (P \Leftrightarrow Q)$  Is Valid Implication i.e. is Tautology.

3. $(P \Leftrightarrow Q) \rightarrow (P \rightarrow Q')$  Is NOT valid implication  i.e. Not tautology.

4. $(P \Leftrightarrow Q') \rightarrow (P \rightarrow Q)$ Is NOT valid implication  i.e. Not tautology.

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[~p ^ (p->q)] - ~p is.,satisfiableunsatisfiabletautologyinvalid