The compound statement $(-(P \wedge Q)) \vee((-P) \wedge Q) \Rightarrow((-P) \wedge(-Q))$ is equivalent to
- $((\sim P) \vee Q) \wedge((\sim Q) \vee P)$
- $(\sim Q) \vee P$
- $((-P) \vee Q) \wedge(-Q)$
- $(-P) \vee Q$
The Correct Option is A
Solution and Explanation
Let r=(∼(P∧Q))∨((∼P)∧Q);s= ((∼P)∧(∼Q))
| P | Q | ∼(P∧Q) | (−P)∧Q | r | s | r→s |
|---|---|---|---|---|---|---|
| T | T | F | F | F | F | T |
| T | F | T | F | T | F | F |
| F | T | T | T | T | F | F |
| F | F | T | F | T | T | T |
Option (A) : ((∼P)∨Q)∧((∼Q)∨P)
is equivalent to (not of only P)∧( not of only Q )
=( Both P,Q) and (neither P nor Q)
Top Questions on mathematical reasoning
- In a group of 100 people, 30 speak only English, another 50 speak only Telugu, and another 20 speak both. How many speak at least one language?
- AP LAWCET - 2025
- General Knowledge and Mental Ability
- mathematical reasoning
- Which is the odd number in the series: 2, 4, 8, 10, 16?
- AP LAWCET - 2025
- General Knowledge and Mental Ability
- mathematical reasoning
- Identify the next in the series: AZ, BY, CX, ?
- AP LAWCET - 2025
- General Knowledge and Mental Ability
- mathematical reasoning
- If CAT = 3120, then DOG = ?
- AP LAWCET - 2025
- General Knowledge and Mental Ability
- mathematical reasoning
- If today is Monday, what will be the day after 100 days?
- AP LAWCET - 2025
- General Knowledge and Mental Ability
- mathematical reasoning
Questions Asked in JEE Main exam
- Let $\vec{a}=2\hat{i}-\hat{j}-\hat{k}$, $\vec{b}=\hat{i}+3\hat{j}-\hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}+3\hat{k}$. Let $\vec{v}$ be the vector in the plane of $\vec{a}$ and $\vec{b}$, such that the length of its projection on the vector $\vec{c}$ is $\dfrac{1}{\sqrt{14}}$. Then $|\vec{v}|$ is equal to
- JEE Main - 2026
- Vector Algebra
A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.- JEE Main - 2026
- Solutions
- The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is \(10^{16}\,\text{s}^{-1}\). The wave number of photon 'C' is \(10^{5}\,\text{cm}^{-1}\). The correct order of energy of these photons is:
- JEE Main - 2026
- General Chemistry
- Given below are two statements: Statement I: The increasing order of boiling point of hydrogen halides is HCl<HBr<HI<HF. Statement II: The increasing order of melting point of hydrogen halides is HCl<HBr<HF<HI. In the light of the above statements, choose the correct answer from the options given below:
- JEE Main - 2026
- General Chemistry
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]- JEE Main - 2026
- Ray optics and optical instruments
Concepts Used:
Mathematical Reasoning
Mathematical reasoning or the principle of mathematical reasoning is a part of mathematics where we decide the truth values of the given statements. These reasoning statements are common in most competitive exams like JEE and the questions are extremely easy and fun to solve.
Types of Reasoning in Maths:
Mathematically, reasoning can be of two major types such as:
- Inductive Reasoning - In this, method of mathematical reasoning, the validity of the statement is examined or checked by a certain set of rules, and then it is generalized. The principle of mathematical induction utilizes the concept of inductive reasoning.
- Deductive Reasoning - The principle is the opposite of the principle of induction. Contrary to inductive reasoning, in deductive reasoning, we apply the rules of a general case to a provided statement and make it true for particular statements. The principle of mathematical induction utilizes the concept of deductive reasoning.