MHT CET · Maths · Mathematical Reasoning
The negation of inverse of \(\sim p \rightarrow q\) is
- A \(\sim \mathrm{p} \wedge \mathrm{q}\)
- B \(\sim \mathrm{q} \rightarrow \mathrm{p}\)
- C \(p \wedge(\sim q)\)
- D \(\mathrm{p} \wedge \mathrm{q}\)
Answer & Solution
Correct Answer
(D) \(\mathrm{p} \wedge \mathrm{q}\)
Step-by-step Solution
Detailed explanation
We have \(\sim \mathrm{p} \rightarrow \mathrm{q}\)
Inverse of given statement is
\(
\sim(\sim \mathrm{p}) \rightarrow \sim \text { q i.e. } \mathrm{p} \rightarrow \sim \mathrm{q}
\)
Negation of inverse of given statement is \(\sim(p \rightarrow \sim q)\)
\(
\equiv \sim(\sim p \vee \sim q) \equiv p \wedge q
\)
Inverse of given statement is
\(
\sim(\sim \mathrm{p}) \rightarrow \sim \text { q i.e. } \mathrm{p} \rightarrow \sim \mathrm{q}
\)
Negation of inverse of given statement is \(\sim(p \rightarrow \sim q)\)
\(
\equiv \sim(\sim p \vee \sim q) \equiv p \wedge q
\)
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 distance of the point \((-1,-5,-10)\) from the point of intersection of the line \(\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\) and the plane \(x-y+z=5\) isMHT CET 2023 Medium
- The rate of change volume of a sphere with respect to its surface area when the radius is 5 meters isMHT CET 2022 Medium
- If the sum of the mean and the variance of a Binomial distribution for 5 trials is 1.8 , then the value of \(\mathrm{p}\) isMHT CET 2023 Easy
- If the area of parallelogram, whose diagonals are \(\hat{i}-\hat{j}+2 \hat{k}\) and \(2 \hat{i}+3 \hat{j}+\alpha \hat{k}\) is \(\frac{\sqrt{93}}{2}\) sq. unit, then \(\alpha=\)MHT CET 2025 Medium
- \(\int \sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}} d x=\)
(where \(\mathrm{C}\) is a constant of integration)MHT CET 2022 Hard - If the lines \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-1}{4}\) and \(\frac{x-3}{-1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}\) intersect, then k is equal toMHT CET 2024 Easy
More PYQs from MHT CET
- \(
y=(1+x)\left(1+x^2\right)\left(1+x^4\right) \ldots \ldots \ldots\left(1+x^{2 n}\right) \text {, }
\)
then the value of \(\frac{d y}{d x}\) at \(x=0\) isMHT CET 2023 Medium - The equation of the circle, the end-points of whose diameter are the centres of the circles \(x^{2}+y^{2}-2 x+3 y-3=0\) and \(x^{2}+y^{2}+6 x-12 y-5=0\) isMHT CET 2020 Medium
- An element crystallises in bcc type crystal structure with edge length of unit cell \(300 \mathrm{pm} .\) Calculate radius of element?MHT CET 2020 Medium
- A first order reaction has rate constant \(1 \times 10^{-2} \mathrm{~s}^{-1}\). What time will it take for \(20 \mathrm{~g}\) of reactant to reduce to \(5 \mathrm{~g}\) ?MHT CET 2020 Easy
- Two identical current carrying coils with same centre are placed with their planes perpendicular to each other. If current \(I=\sqrt{2} \mathrm{~A}\) and radius of the coil is \(\mathrm{R}=1 \mathrm{~m}\), then magnetic field at centre is equal to ( \(\mu_0=\) permeability of free space)MHT CET 2024 Medium
- In a triangle ABC with usual notations, if \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are in arithmetic progression, then, \(\tan \frac{A}{2} \cdot \tan \frac{C}{2}=\)MHT CET 2025 Medium