MHT CET · Maths · Mathematical Reasoning
If p, q, r, s are statements, where, \(p: A^2-B^2=(A-B)(A+B) ; A, B\) are matrices, \(A B \neq B A\)
q: \(5 \leqslant 5\)
r: \({ }^8 \mathrm{C}_1+{ }^8 \mathrm{C}_2+{ }^8 \mathrm{C}_3+\ldots \ldots \ldots . .+{ }^8 \mathrm{C}_8=256\)
s: Maximum value of \({ }^8 \mathrm{C}_{\mathrm{r}}\) is 70 then the statement from the following having truth value true is ....
- A \((\mathrm{p} \wedge \sim \mathrm{r}) \vee(\sim \mathrm{q} \wedge \sim \mathrm{s})\)
- B \((\mathrm{p} \vee \sim q) \leftrightarrow(\sim \mathrm{r} \rightarrow \mathrm{s})\)
- C \((\mathrm{p} \leftrightarrow \mathrm{q}) \wedge(\sim \mathrm{p} \vee \sim \mathrm{q})\)
- D \((\mathrm{s} \vee \sim \mathrm{p}) \leftrightarrow(\sim \mathrm{p} \wedge \sim \mathrm{r})\)
Answer & Solution
Correct Answer
(D) \((\mathrm{s} \vee \sim \mathrm{p}) \leftrightarrow(\sim \mathrm{p} \wedge \sim \mathrm{r})\)
Step-by-step Solution
Detailed explanation
Truth values: \(p: (A-B)(A+B) = A^2+AB-BA-B^2\). For \(A^2-B^2=(A-B)(A+B)\), \(AB\) must equal \(BA\). Given \(AB \neq BA\), so \(p\) is False (F).
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