Consider the following statements:
P : I have fever
Q: I will not take medicine
R : I will take rest
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:
P : I have fever
Q: I will not take medicine
R : I will take rest
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:
- $(P \vee Q) \wedge((\sim P) \vee R)$
- $(P \vee \sim Q) \wedge(P \vee \sim R)$
- $((\sim P) \vee \sim Q) \wedge((\sim P) \vee \sim R)$
$((\sim P) \vee \sim Q)\wedge((\sim P) \vee R)$
The Correct Option is D
Solution and Explanation
So, the correct answer is (D) : $((\sim P) \vee \sim Q) \vee((\sim P) \vee R)$
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Questions Asked in JEE Main exam
Let $ A \in \mathbb{R} $ be a matrix of order 3x3 such that $$ \det(A) = -4 \quad \text{and} \quad A + I = \left[ \begin{array}{ccc} 1 & 1 & 1 \\2 & 0 & 1 \\4 & 1 & 2 \end{array} \right] $$ where $ I $ is the identity matrix of order 3. If $ \det( (A + I) \cdot \text{adj}(A + I)) $ is $ 2^m $, then $ m $ is equal to:
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- An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m\(^3\). If the pressure inside the bubble is 2100 N/m\(^2\) greater than the atmospheric pressure, then the surface tension of the liquid in SI units is (use \(g = 10 \, {m/s}^2\)).
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- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
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A square loop of sides \( a = 1 \, {m} \) is held normally in front of a point charge \( q = 1 \, {C} \). The flux of the electric field through the shaded region is \( \frac{5}{p} \times \frac{1}{\varepsilon_0} \, {Nm}^2/{C} \), where the value of \( p \) 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.