Negation of the statement "The payment will be made if and only if the work is finished in time." is

Negation of the statement "The payment will be made if and only if the work is finished in time." is
  1. The work is finished in time and the payment is not made.
  2. The payment is made and the work is not finished in time.
  3. 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. 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.

Solution

Let p : Payment will be made q : Work is finished in time. Given statement is $(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{p})$
Negation of above statement is $(p \wedge \sim q) \vee(q \wedge \sim p)$ $\therefore \quad$ Option (D) is correct.

Asked in: MHT CET 2024 (10 May Shift 1)

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