Negation of an 'if and only if' (biconditional) statement

1. A.
   Horses have wings but crows do not have tails. or crows have tails but horses do not have wings.
2. B.
   Horses do not have wings if and only if crows do not have tails.
3. C.
   Horses do not have wings and crows have tails. or Horses have wings and crows have tails.
4. D.
   Horses do not have wings and crows do not have tails.

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1. A.
   The work is finished in time and the payment is not made.
2. B.
   The payment is made and the work is not finished in time.
3. C.
   The work is finished in time and the payment is not made, or the payment is made and the work is finished in time.
4. D.
   Either the work is finished in time and the payment is not made, or the payment is made and the work is not finished in time.

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1. A.
   equivalent to $p \leftrightarrow q$
2. B.
   a fallacy
3. C.
   a tautology
4. D.
   equivalent to $\sim p \leftrightarrow q$

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1. A.
   The work is finished in time and the payment is not made.
2. B.
   The payment is made and the work is not finished in time.
3. C.
   The work is finished in time and the payment is not made, or the payment is made and the work is finished in time.
4. D.
   Either the work is finished in time and the payment is not made, or the payment is made and the work is not finished in time.

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1. A.
   The number is an odd number but not divisible by 3 or the number is divisible by 3 but not odd.
2. B.
   The number is not an odd number if it is not divisible by 3.
3. C.
   The number is not an odd number but it is divisible by 3.
4. D.
   The number is not an odd number or is not divisible by 3 but the number is divisible by 3 or odd.

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1. A.
   $\sim p \to q$
2. B.
   $\sim p \leftrightarrow \sim q$
3. C.
   $\sim(q \to \sim p)$
4. D.
   $p \leftrightarrow \sim q$

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