\(\sim\left(p\, \vee\, \sim q\right) \rightarrow p\, \vee\, q\)
\(\left(\sim p \wedge q\right) \to p \vee q\)
\(\sim\left\{\left(\sim p \wedge q\right)\wedge \left(\sim p \wedge \sim q\right)\right\}\)
\(\sim\left(\sim p \wedge f\right)\)
So, the correct option is (D): \(\sim\left(p\, \vee\, \sim q\right) \rightarrow p\, \vee\, q\).
In the (4 times 4) array shown below, each cell of the first three rows has either a cross (X) or a number. The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is:
Let \( \{(a, b) : a, b \in {R, a<b \} }\) be a basis for a topology \( \tau \) on \( {R} \). Which of the following is/are correct?
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32
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.
Mathematically, reasoning can be of two major types such as: