Consider the statements given by following : (A) If $3+3=7$, then $4+3=8$. (B) If $5+3=8$, then earth is…

Consider the statements given by following : (A) If $3+3=7$, then $4+3=8$. (B) If $5+3=8$, then earth is flat. (C) If both $(\mathrm{A})$ and $(\mathrm{B})$ are true, then $5+6=17$. Then which of the following statements is correct?
  1. (A) is true while (B) and (C) are false.
  2. (A) and (C) are true while (B) is false.
  3. (A) and (B) are false, while (C) is true.
  4. (A) is false but (B) and (C) are true.

Solution

(A). Let $\mathrm{p}: 3+3=7$ $q: 4+3=8$
Truth value of p and q are F and F . $\therefore \quad \mathrm{p} \rightarrow \mathrm{q} \equiv \mathrm{T}$ (B) Let $\mathrm{p}: 5+3=8$, q ; earth is flat Truth value of p and q are T and F . $\therefore \quad \mathrm{p} \rightarrow \mathrm{q} \equiv \mathrm{F}$. (C) Let p : Both (A) and (B) are true $q: 5+6=17$
Truth values of $p, q$ are false and false. $\therefore \quad \mathrm{p} \rightarrow \mathrm{q} \equiv \mathrm{~T}$ $\therefore \quad(\mathrm{A})$ and $(\mathrm{C})$ are true, while $(B)$ is false.

Asked in: MHT CET 2024 (09 May Shift 1)

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