Consider the following statements.
$p$: If $3^4 > 4^3$, then $3^3 > 4^4$
$q$: The roots of the equation $x^2-2x+2 = 0$ are real if and only if Mumbai is in Maharashtra.
$r$: Statement $p$ is true or statement $q$ is false.
Which of the following has truth value T (true)?

Question

If $ x \neq 0 $, then \[ \frac{\sin(\pi + x)\cos\left(\frac{\pi}{2} + x\right)\tan\left(\frac{3\pi}{2} - x\right)\cot(2\pi - x)}{\sin(2\pi - x)\cos(2\pi + x)\csc(-x)\sin\left(\frac{3\pi}{2} + x\right)} = \]

Answer 1

Step 1: Evaluate the parts:
p: implication with true hypothesis and false conclusion, false. q: "roots real" is false, "Mumbai in Maharashtra" is true, and the biconditional of false and true is false. r: $p \lor \sim q$, with $\sim q = T$, is true.

Step 2: Table of values:
p = F, q = F, r = T.

Step 3: Check each option quickly:
Any option that needs p or q to be true on its own, or both p and q, fails except where r alone can carry the disjunction. Only $(p \land q) \lor r$ has r as a free disjunct, so it is $F \lor T = T$. The others reduce to F.

Final Answer:
Option (D) has truth value T. \[ \boxed{(p\wedge q)\vee r} \]

Consider the following statements.
\(p\): If \(3^4 > 4^3\), then \(3^3 > 4^4\)
\(q\): The roots of the equation \(x^2-2x+2 = 0\) are real if and only if Mumbai is in Maharashtra.
\(r\): Statement \(p\) is true or statement \(q\) is false.
Which of the following has truth value T (true)?

Show Hint

The Correct Option is D

Solution and Explanation

Top Questions on Statements

Questions Asked in MHT CET exam

Consider the following statements.\(p\): If \(3^4 > 4^3\), then \(3^3 > 4^4\)\(q\): The roots of the equation \(x^2-2x+2 = 0\) are real if and only if Mumbai is in Maharashtra.\(r\): Statement \(p\) is true or statement \(q\) is false.Which of the following has truth value T (true)?