MHT CET · Maths · Mathematical Reasoning
\(\sim[(p \vee \sim q) \rightarrow(p \wedge \sim q)] \equiv\)
- A \((p \wedge \sim q) \wedge(\sim p \vee q)\)
- B \((p \wedge \sim q) \wedge(\sim p \wedge q)\)
- C \((p \vee \sim q) \wedge(\sim p \vee q)\)
- D \((p \vee \sim q) \vee(\sim p \vee q)\)
Answer & Solution
Correct Answer
(C) \((p \vee \sim q) \wedge(\sim p \vee q)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sim[(p \vee \sim q) \rightarrow(p \wedge \sim q)] \\ & \equiv \sim[\sim(p \vee \sim q) \vee(p \wedge \sim q)] \ldots[\text { Conditional law }]\end{aligned}\)
\(\begin{array}{ll}\equiv(p \vee \sim q) \wedge \sim(p \wedge \sim q) & \ldots[\text { De Morgan's law }] \\ \equiv(p \vee \sim q) \wedge(\sim p \vee q) & \ldots[\text { De Motgan's law }]\end{array}\)
\(\begin{array}{ll}\equiv(p \vee \sim q) \wedge \sim(p \wedge \sim q) & \ldots[\text { De Morgan's law }] \\ \equiv(p \vee \sim q) \wedge(\sim p \vee q) & \ldots[\text { De Motgan's law }]\end{array}\)
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 co-ordinates of the points on the line \(\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}\) at a distance of 12 units from the point \(\mathrm{A}(-2,1,-1)\) areMHT CET 2021 Medium
- If the vectors \(\hat{i}+2 \hat{\jmath}+x \hat{k}\) and \(y t+6 \hat{k}+4 \hat{k}\) are collinear, then the values of \(x\) and
\(y\) are respectively,MHT CET 2020 Easy - The sum of the first terms of the series isMHT CET 2018 Hard
- The number of discontinuities of the greatest integer function \(\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)\)MHT CET 2023 Easy
- If the function \(\mathrm{f}(x)=\left\{\begin{array}{cl}\frac{\cos a x-\cos b x}{\cos c x-\cos b x} & , \text { if } x \neq 0 \\ -1 & , \text { if } x=0\end{array}\right.\) is continuous at \(x=0\), then \(a^2, b^2, c^2\) are inMHT CET 2025 Medium
- If \(4 \sin ^{-1} x+\cos ^{-1} x=\pi\) then \(x=\)MHT CET 2025 Easy
More PYQs from MHT CET
- In an adiabatic process for an ideal gas, the relation between the universal gas constant ' \(R\) ' and specific heat at constant volume ' \(\mathrm{C}_{\mathrm{v}}\) ' is \(R=0 \cdot 4 C_v\). The pressure ' \(P\) ' of the gas is proportional to the temperature ' T ', of the gas as \(\mathrm{T}^k\). The value of constant ' K ' isMHT CET 2024 Hard
- What is the volume of a gas at \(1.032 \times 10^5 \mathrm{Nm}^{-2}\) if it occupies \(1 \mathrm{dm}^3\) of volume at normal temperature and pressure?MHT CET 2024 Easy
- A pendulum is oscillating with frequency ' \(n\) ' on the surface of earth. If it is taken to a depth \(\frac{R}{4}\) below the surface of earth, new frequency of oscillation of depth \(\frac{R}{4}\) is ( \(R=\) radius of earth)MHT CET 2024 Easy
- What is the conductivity of \(0.02 \mathrm{M} \mathrm{KCl}\) solution if cell constant is \(1.29 \mathrm{~cm}^{-1}\) with resistance \(645 \Omega\) ?MHT CET 2021 Hard
- Which one of the following is measured in Dobson units (DU)?MHT CET 2025 Easy
- What is the packing efficiency of silver metal in its unit cell?MHT CET 2023 Easy