MHT CET · Maths · Mathematical Reasoning
The logical statement \([\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r}) \wedge(\sim \mathrm{q} \wedge \mathrm{r})]\) is equivalent to
- A \((p \wedge r) \wedge \sim q\)
- B \((\sim \mathrm{p} \wedge \sim \mathrm{q}) \wedge \mathrm{r}\)
- C \(\sim \mathrm{p} \vee \mathrm{r}\)
- D \((p \wedge \sim q) \vee r\)
Answer & Solution
Correct Answer
(A) \((p \wedge r) \wedge \sim q\)
Step-by-step Solution
Detailed explanation
\(\sim(\sim \mathrm{p} \vee \mathrm{q}) \equiv \mathrm{p} \wedge \sim \mathrm{q}\) \([\ (\mathrm{p} \wedge \sim \mathrm{q}) \vee (\mathrm{p} \wedge \mathrm{r}) \ ] \wedge (\sim \mathrm{q} \wedge \mathrm{r})\)
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 equation of a circle, which passes through the centre of the circle \(x^2+y^2+8 x+10 y-7=0\) and is concentric with the circle. \(2 x^2+2 y^2-8 x-12 y-9=0\), isMHT CET 2022 Easy
- The equation of a line, whose perpendicular distance from the origin is 5 units and the angle, which the perpendicular to the line from the origin makes, is \(210^{\circ}\) with positive \(\mathrm{X}\)-axis, isMHT CET 2022 Easy
- If the vectors and are collinear then the value of is equalMHT CET 2019 Easy
- The vector equation of the line \(2 x+4=3 y+1=6 z-3\) isMHT CET 2023 Easy
- \(\int_{0}^{\pi / 2} \frac{\sin x-\cos x}{1-\sin x \cdot \cos x} d x\) is equal toMHT CET 2009 Easy
- Let \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) be three vectors such that \(|\overline{\mathrm{a}}|=\sqrt{3}\), \(|\bar{b}|=5, \bar{b} \cdot \bar{c}=10\) and the angle between \(\bar{b}\) and \(\bar{c}\) is \(\frac{\pi}{3}\). If \(\overline{\mathrm{a}}\) is perpendicular to the vector \(\overline{\mathrm{b}} \times \overline{\mathrm{c}}\), then \(|\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})|\) is equal toMHT CET 2023 Medium
More PYQs from MHT CET
- A body weighs \(300 \mathrm{~N}\) on the surface of the earth. How much will it weigh at a distance \(\frac{R}{2}\) below the surface of earth? ( \(\mathrm{R} \rightarrow\) Radius of earth)MHT CET 2023 Easy
- The Cartesian equation of the plane passing through the point A \((7,8,6)\) and parallel to the XY plane isMHT CET 2021 Easy
- Two springs have spring constant \(k_{A}\) and \(k_{B}\) and \(k_{A}>k_{B}\). The work required to stretch them by same extension will beMHT CET 2011 Easy
- The kinetic energy of the electron in an orbit of radius \(r\) in hydrogen atom is proportional to ( \(e=\) electronic charge \()\)MHT CET 2022 Medium
- Identify the product when phenol is heated with zinc dust.MHT CET 2023 Easy
- What is the formal charge on ' \(\mathrm{N}\) ' atom in \([: \ddot{\mathrm{S}}-\mathrm{C} \equiv \mathrm{N} \text { : }]^{\ominus}\) ion?MHT CET 2021 Medium