The statement
\((∼(p ⇔∼q))∧q \)
is :
The statement
\((∼(p ⇔∼q))∧q \)
is :
- A tautology
- A contradiction
\(Equivalent\ to\ (p⇒q)∧q\)
\(Equivalent\ to\ (p⇒q)∧p\)
The Correct Option is D
Solution and Explanation
\(∼(p⇔ ∼q)∧q\)
\(=(p⇔q)∧q\)
So, the correct option is (D): \(Equivalent\ to\ (p⇒q)∧q\)
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 one focus of the hyperbola \( H : \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1 \) be at \( (\sqrt{10}, 0) \) and the corresponding directrix be \( x = \dfrac{9}{\sqrt{10}} \). If \( e \) and \( l \) respectively are the eccentricity and the length of the latus rectum of \( H \), then \( 9 \left(e^2 + l \right) \) is equal to:
- JEE Main - 2025
- Conic sections
- Let \( \alpha_1 \) and \( \beta_1 \) be the distinct roots of \( 2x^2 + (\cos\theta)x - 1 = 0, \ \theta \in (0, 2\pi) \). If \( m \) and \( M \) are the minimum and the maximum values of \( \alpha_1 + \beta_1 \), then \( 16(M + m) \) equals:
- JEE Main - 2025
- Maxima and Minima
- Let the line \( x + y = 1 \) meet the circle \( x^2 + y^2 = 4 \) at the points A and B. If the line perpendicular to AB and passing through the midpoint of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to:
- JEE Main - 2025
- Coordinate Geometry
- The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:
- JEE Main - 2025
- permutations and combinations
- Two identical symmetric double convex lenses of focal length \( f \) are cut into two equal parts \( L_1, L_2 \) by the AB plane and \( L_3, L_4 \) by the XY plane as shown in the figure respectively. The ratio of focal lengths of lenses \( L_1 \) and \( L_3 \) is:
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.