MHT CET · Maths · Mathematical Reasoning
For the simple statements \(p, q\), and \(r, p \rightarrow(q \vee r)\) is logically equivalent to
- A \((p \vee q) \rightarrow r\)
- B \((p \rightarrow q) \vee(p \rightarrow r)\)
- C \((p \rightarrow \sim q) \wedge(p \rightarrow r)\)
- D \((p \rightarrow q) \wedge(p \rightarrow \sim r)\)
Answer & Solution
Correct Answer
(B) \((p \rightarrow q) \vee(p \rightarrow r)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & P \rightarrow(q \vee r) \\ & \equiv \sim p \vee(q \vee r) \quad[\because p \rightarrow q \equiv \sim p \vee q] \\ & \equiv(\sim p \vee q) \vee(\sim p \vee r) \\ & \equiv(p \rightarrow q) \vee(p \rightarrow r)\end{aligned}\)
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
- If the equation \(\mathrm{k} x y+10 x+8 \mathrm{y}+16=0\) represents a pair of lines, thenMHT CET 2025 Medium
- An urn contains 9 balls of which 3 are red, 4 are blue and 2 are green. Three balls are drawn at random from the urn. The probability that the three balls have difference colours isMHT CET 2021 Medium
- If the lines giviven by \(\frac{x-1}{2 \lambda}=\frac{y-1}{-5}=\frac{z-1}{2}\) and \(\frac{x+2}{\lambda}=\frac{y+3}{\lambda}=\frac{z+5}{1}\) are parallel, then the value\epsiloneMHT CET 2020 Easy
- If \(\cot (A+B)=0\), then \(\sin (A+2 B)\) is equal toMHT CET 2022 Easy
- The area bounded between the curve \(x^2=y\) and the line \(y=4 x\) isMHT CET 2021 Easy
- The maximum area of the rectangle that can be inscribed in a circle of radius \(r\), isMHT CET 2007 Medium
More PYQs from MHT CET
- Charges of \(2 \mu \mathrm{C}\) and \(-3 \mu \mathrm{C}\) are placed at two points \(A\) and \(B\) separated by distance of 1 m . The distance of the point from \(A\) where net potential is zero isMHT CET 2025 Medium
- Figure shows triangular lamina which can rotate about different axes. Moment of inertia is maximum, about the axis
MHT CET 2021 Hard - The equation of the common tangent touching the circle \((x-3)^2+\mathrm{y}^2=9\) and the parabola \(\mathrm{y}^2=4 x\) above the X -axis isMHT CET 2025 Hard
- Following graph shown the variation of stopping potential corresponding to the frequency of incident radiation \((v)\) for a given metal. The correct variation is shown in graph [ \(v_0=\) threshold frequency]
MHT CET 2022 Easy - The rate law for the reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\) at \(25^{\circ} \mathrm{C}\) is given by rate \(=k[A][B]^2\). Calculate the rate of reaction if rate constant at same temperature is \(6.25 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}[[\mathrm{~A}]=1 \mathrm{M},[\mathrm{B}]=0.2 \mathrm{M}]\)MHT CET 2023 Medium
- Select the group of CORRECT statements.
I. If phenotype of offsprings shows only the dominant trait then the parent plants are heterozygous.
II. A true breeding line shows stable trait inheritance and expression for several generations.
III. In mendelian experiment material, contrasting characters can be easily recognized.
IV. When a single gene controls two (or more) different traits, it is called polygene.
V. When interactions occurs between the alleles of different genes present on the same or different chromosome it is called intragenic interaction.MHT CET 2025 Hard