The verbal statement of the same meaning, of the statement 'If the grass is green then it rains in July' is

The verbal statement of the same meaning, of the statement 'If the grass is green then it rains in July' is
  1. The grass is not green and it does not rains in July.
  2. The grass is not green or it rains in July.
  3. If the grass is not green, then it does not rain in July.
  4. The grass is not green if and only if it rains in July.

Solution

Let $p:$ The grass is green $\mathrm{q}$ : If rains in July. The logical form of given statement is $\mathrm{p} \rightarrow \mathrm{q}$ We know that $\mathrm{p} \rightarrow \mathrm{q} \equiv \sim \mathrm{p} \vee \mathrm{q}$ The grass is not green or it rains in July.

Asked in: MHT CET 2020 (15 Oct Shift 1)

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