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Which one of the following Boolean expressions is NOT a tautology?

  1. $((\,a\,\to\,b\,)\,\wedge\,(\,b\,\to\,c))\,\to\,(\,a\,\to\,c)$
  2. $(\,a\,\to\,c\,)\,\to\,(\,\sim b\,\to\,(a\,\wedge\,c))$
  3. $(\,a\,\wedge\,b\,\wedge\,c)\,\to\,(\,c\vee\,a)$
  4. $a\,\to\,(b\,\to\,a)$
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we can also solve it by satisfying the T(try to make LHS true) and F(try to make RHS False) condition of ->(implication), if it satisfied then it is NOT tautology. if it is not then it is Tautology. Answer is B
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