Negation of the statement ' Horses have wings if and only if crows have tails. ' is

Negation of the statement ' Horses have wings if and only if crows have tails. ' is
  1. Horses have wings but crows do not have tails. or crows have tails but horses do not have wings.
  2. Horses do not have wings if and only if crows do not have tails.
  3. Horses do not have wings and crows have tails. or Horses have wings and crows have tails.
  4. Horses do not have wings and crows do not have tails.

Solution

Let p : Horses have wings q : Crows have tails Given statement is $\mathrm{p} \leftrightarrow \mathrm{q}$ $\sim(p \leftrightarrow q) \equiv(p \wedge \sim q) \vee(q \wedge \sim p)$

Asked in: MHT CET 2024 (09 May Shift 2)

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