MHT CET · Maths · Mathematical Reasoning
The negation of the statement \((p \wedge q) \rightarrow(\sim p \vee r)\) is
- A \(\mathrm{p} \vee \mathrm{q} \vee \sim \mathrm{r}\)
- B \(\mathrm{p} \wedge \mathrm{q} \wedge \approx \mathrm{r}\)
- C \(\sim p \vee q \wedge r\)
- D \(\sim \mathrm{p} \vee \sim \mathrm{q} \vee \sim \mathrm{r}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{p} \wedge \mathrm{q} \wedge \approx \mathrm{r}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sim[(p \wedge q) \rightarrow(\sim p \vee r)] \\ & \equiv(p \wedge q) \wedge \sim(\sim p \vee r) \ldots[\because \sim(p \rightarrow q) \equiv p \wedge \sim q] \\ & \equiv p \wedge q \wedge p \wedge \sim r \quad \ldots[\text { Associative Law }] \\ & \equiv p \wedge q \wedge \sim r \quad \ldots[\text { Idempotent Law }]\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The measure of the acute angle between the lines given by the equation
\(3 x^{2}-4 \sqrt{3} x y+3 y^{2}=0\) isMHT CET 2020 Medium - \(\mathrm{F}(\mathrm{x})=\log |\sin \mathrm{x}|\), where \(\mathrm{x} \in(0, \pi)\) is strictly increasing onMHT CET 2021 Medium
- In a triangle ABC , with usual notations, if \(a=5, \mathrm{~b}=7, \sin \mathrm{~A}=\frac{3}{4}\), then total number of triangles possible areMHT CET 2025 Medium
- If the points \(A(5, k), B(-3,1)\) and \(C(-7,-2)\) are collinear, then \(\mathrm{k}=\)MHT CET 2020 Easy
- with usual notations, if triangle \(\mathrm{ABC}\) is right angled at \(\mathrm{C}\), then \(\left(\frac{\mathrm{a}^{2}+\mathrm{b}^{2}}{\mathrm{a}^{2}-\mathrm{b}^{2}}\right) \sin (\mathrm{A}-\mathrm{B})=\)MHT CET 2020 Medium
- Let \(f^{\prime}(0)=-3\) and \(f^{\prime}(x) \leq 5\) for all real values of \(x\). The \(\mathrm{f}(2)\) can have possible maximum value asMHT CET 2023 Medium
More PYQs from MHT CET
- Given below are two statements.
Statement I - The amount of energy available in an ecosystem increases at each successive trophic level.
Statement II - Transfer of energy from one trophic level to the other follows 10% law.
In the light of above statements, select the correct option given below:MHT CET 2025 Easy - A uniform circular disc of mass \(12 \mathrm{~kg}\) is held by two identical springs. When the disc is slightly pressed down and released, it executes S.H.M. of period 2 second. The force constant of each spring is (nearly) (Take \(\pi^2=10\) )
MHT CET 2023 Medium - Based on following statements choose the correct option given below.
Statement I: Dormancy is a state of metabolic arrest that facilitates the survival of seeds during unfavourable conditions.
Statement II: Mature and viable seeds do not germinate even in the presence of favourable conditions unless the dormancy period is completed.MHT CET 2021 Hard - A null point is obtained at 200 cm on potentiometer wire when cell in secondary circuit is shunted by \(5 \Omega\). When a resistance of \(15 \Omega\) is used for shunting, null point moves to 300 cm . The internal resistance of the cell isMHT CET 2025 Easy
- Let \(\vec{a}=\hat{i}-2 \hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}-\hat{j}+\hat{k}\) be two vectors. If \(\vec{c}\) is a vector such that \(\vec{b} \times \vec{c}=\vec{b} \times \vec{a}\) and \(\vec{c} \cdot \vec{a}\) then \(\vec{c} \cdot \vec{b}\) is equal toMHT CET 2022 Medium
- The discrete random variable \(\mathrm{X}\) can take all possible integer values from 1 to \(\mathrm{k}\), each with a probability \(\frac{1}{\mathrm{k}}\), then its variance isMHT CET 2023 Easy