The inverse of the proposition $(p \wedge \sim q)\rightarrow r$ is
- $(\sim\,r) \rightarrow(\sim p) \vee q$
- $(\sim p) \vee q \rightarrow (\sim r)$
- $r \rightarrow p \wedge(\sim q) $
- $(\sim p)\vee(\sim q) \rightarrow r $
The Correct Option is B
Solution and Explanation
$(p \wedge \sim q) \rightarrow r\,\,\,\,\,\,...(i)$
Inverse of E (i) is
$\sim(p \wedge \sim q) \rightarrow \sim r $
$\equiv \sim p \vee q \rightarrow \sim r$
$\equiv(\sim p) \vee q \rightarrow(\sim r)$
Top Questions on mathematical reasoning
- 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: 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?
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?
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?
- The value of the contour integral $\oint \frac{dz}{2z - z^2}$ along the circle $|z| = 1$, oriented in the counterclockwise sense is
- GATE NM - 2024
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Questions Asked in KCET exam
- Which of the following statements is/are true about equilibrium?
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A block of certain mass is placed on a rough floor. The coefficients of static and kinetic friction between the block and the floor are 0.4 and 0.25 respectively. A constant horizontal force \( F = 20 \, \text{N} \) acts on it so that the velocity of the block varies with time according to the following graph. The mass of the block is nearly (Take \( g = 10 \, \text{m/s}^2 \)):
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- A random experiment has five outcomes \(w_1, w_2, w_3, w_4, w_5\). The probabilities of the occurrence of the outcomes \(w_1, w_2, w_4, w_5\) are respectively \( \frac{1}{6}, a, b, \frac{1}{12} \) such that \(12a + 12b - 1 = 0\). Then the probabilities of occurrence of the outcome \(w_3\) is:
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A wooden block of mass M lies on a rough floor. Another wooden block of the same mass is hanging from the point O through strings as shown in the figure. To achieve equilibrium, the coefficient of static friction between the block on the floor and the floor itself is
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The circuit shown in the figure contains two ideal diodes \( D_1 \) and \( D_2 \). If a cell of emf 3V and negligible internal resistance is connected as shown, then the current through \( 70 \, \Omega \) resistance (in amperes) is:
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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.