The statement $p \rightarrow \left(\sim q\right)$ is equivalent to
- $q \to p$
- $\sim q \, \vee\, \sim\,p$
- $p \,\wedge\, \sim\,q$
- $\sim q \to p$
The Correct Option is B
Solution and Explanation
Top Questions on mathematical reasoning
For the clock shown in the figure, if
O = O Q S Z P R T, and
X = X Z P W Y O Q,
then which one among the given options is most appropriate for P?
- GATE ST - 2025
- General Aptitude
- mathematical reasoning
A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained:
(i) The sum of Yellow balls and twice the number of Violet balls is 50.
(ii) The sum of Violet and Green balls is 50.
(iii) The sum of Yellow and Red balls is 50.
(iv) The sum of Violet and twice the number of Red balls is 50.
Which one of the following Pie charts correctly represents the balls in the bag?
- GATE ST - 2025
- General Aptitude
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In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively?
- GATE ST - 2025
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- Consider a five-digit number PQRST that has distinct digits P, Q, R, S, and T, and satisfies the following conditions:
1. \( P<Q \)
2. \( S>P>T \)
3. \( R<T \)
If integers 1 through 5 are used to construct such a number, the value of P is:- GATE ST - 2025
- General Aptitude
- mathematical reasoning
- The number of different permutations of all the letters of the word "PERMUTATION" such that any two consecutive letters in the arrangement are neither both vowels nor both identical is:
- VITEEE - 2024
- Mathematics
- mathematical reasoning
Questions Asked in KEAM exam
For the reaction:
$3Fe_{(s)} + 2O_2{(g)} \rightarrow Fe_3O_4{(s)}$
$\Delta H = -1650\,\text{kJ mol}^{-1}$, $\Delta S = -600\,\text{J K}^{-1} \text{mol}^{-1}$ at $300\,\text{K}$. What is the value of free energy change for the reaction at $300\,\text{K}$?
- KEAM - 2024
- Thermodynamics
- For the reaction: $$ 2A + B \rightarrow 2C + D $$ The following kinetic data were obtained for three different experiments performed at the same temperature: $$ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline \text{I} & 0.10 & 0.10 & 0.10 \\ \text{II} & 0.20 & 0.10 & 0.40 \\ \text{III} & 0.20 & 0.20 & 0.40 \\ \hline \end{array} $$ The total order and order in $[B]$ for the reaction are respectively:
- KEAM - 2024
- Grignard’s reagents and their uses
- Torque on a coil carrying current \( I \) having \( N \) turns and area of cross section \( A \) when placed with its plane perpendicular to a magnetic field \( B \) is:
- KEAM - 2024
- Magnitude and Directions of a Vector
- The line joining the points $ (2,2,2) $ and $ (6,6,6) $ meets the line $$ \frac{x - 1}{3} = \frac{y - 2}{2} = \frac{z - 5}{-1} $$ at the point
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- Coordinate Geometry
- Simplify the following expression: \[ \cos 18^\circ \cos 42^\circ \cos 78^\circ. \] The simplified form is:
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- Various Forms of the Equation of a Line
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.