MHT CET · Maths · Mathematical Reasoning
If \(p \rightarrow(q \vee r)\) is false, then the truth values of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) are respectively
- A F,F,F
- B T, T, F
- C T, F, F
- D \(\mathrm{F}, \mathrm{T}, \mathrm{T}\)
Answer & Solution
Correct Answer
(C) T, F, F
Step-by-step Solution
Detailed explanation
Since \(p \rightarrow q\) is false, when \(p\) is true and \(q\) is false.
\(\mathrm{p} \rightarrow(\mathrm{q} \vee \mathrm{r})\) is false,
\(\therefore \quad \mathrm{p}\) is true and \(\mathrm{q} \vee \mathrm{r}\) is false
\(\Rightarrow p\) is true and both \(q\) and \(r\) are false.
\(\mathrm{p} \rightarrow(\mathrm{q} \vee \mathrm{r})\) is false,
\(\therefore \quad \mathrm{p}\) is true and \(\mathrm{q} \vee \mathrm{r}\) is false
\(\Rightarrow p\) is true and both \(q\) and \(r\) are false.
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 orthocenter of the triangle formed by the lines \(x-2 y=10\) and \(6 x^2+x y-y^2=0\) isMHT CET 2022 Medium
- The area of the region bounded by the curves \(x^{2}+y^{2}=8\) and
\(y^{2}=2 x\) isMHT CET 2012 Medium - If \(\left|\frac{\mathrm{z}}{1+\mathrm{i}}\right|=2\), where \(\mathrm{z}=x+\mathrm{i} y, \mathrm{i}=\sqrt{-1}\) represents a circle, then centre ' \(C\) ' and radius ' \(r\) ' of the circle areMHT CET 2024 Hard
- The lines \(x+2 a y+a=0, x+3 b y+b=0, x+4 c y+c=0\) are concurrent then \(a, \mathrm{~b}, \mathrm{c}\) are inMHT CET 2025 Medium
- \(\tan \left\{\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right\}\) has the valueMHT CET 2022 Easy
- Let \(y=y(x)\) be the solution of the differential equation \(x \frac{\mathrm{~d} y}{\mathrm{~d} x}+y=x \log x,(x\gt1)\)
If \(2(y(2))=\log 4-1\) then the value of \(y(\mathrm{e})\) isMHT CET 2024 Hard
More PYQs from MHT CET
- Match the enzyme in Column I with its role in Column II:
Column I Column II 1. Ligase a. Peptide bond formation 2. Ribozyme b. Hydrolysis of lactose 3. Permease c. Joining of okazaki fragments 4. \(\beta\) - galactosidase d. Increases permeability
Choose the correct answer from the following options.MHT CET 2025 Easy - A rope is wound around a solid cylinder of mass \(1 \mathrm{~kg}\) and radius \(0 \cdot 4 \mathrm{~m}\). What is the angular acceleration of cylinder, if the rope is pulled with a force of \(25 \mathrm{~N} ?\)
(cylinder is rotating about its own axis)MHT CET 2020 Easy - Which does not react with Fehling's solution?MHT CET 2007 Medium
- A potentiometer wire of length \(100 \mathrm{~cm}\) and resistance \(3 \Omega\) is connected in series
with resistance of \(8 \Omega\) and an accumulator of 4 volt whose internal resistance is
\(1 \Omega\)
A cell of e.m.f. 'E' is balanced by \(50 \mathrm{~cm}\) length of the wire. The e.m.f. of the
cell isMHT CET 2020 Medium - Mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3 , then new variance of the resulting observations isMHT CET 2023 Easy
- For a ray of light, the critical angle is minimum, when it travels fromMHT CET 2024 Easy