List of top Mathematics Questions on Mathematical Logic asked in MHT CET

Consider the following logical statements:
R: If \(p \rightarrow q\) is false, then \(p \vee q\) is false.
S: If \(p \leftrightarrow q\) is false, then \(p \vee q\) is false.
Evaluate the truth values of R and S.

If the statement $(p \wedge q) \rightarrow (r \vee \neg s)$ is False (F), then the truth values of $p, q, r$ and $s$ are respectively

Identify the truth value of the statement pattern \( (p \land \sim q) \rightarrow r \).

\( \int_{0}^{1} \log (\frac{1}{x} - 1) dx = \)}

The differential equation whose solution is \( Ax^2 + By^2 = 1 \), where A and B are arbitrary constants is of}

$\int \frac{\sin 2x}{(a+b\cos x)^2} dx =$

If $3 \sin \alpha = 5 \sin \beta$, then $\tan \left( \frac{\alpha+\beta}{2} \right) + \tan \left( \frac{\alpha-\beta}{2} \right) =$

The circumradius of the triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is

If $\bar{p} = 2\hat{\text{i}} + \hat{\text{k}}, \bar{q} = \hat{\text{i}} + \hat{\text{j}} + \hat{\text{k}}, \bar{r} = 4\hat{\text{i}} - 3\hat{\text{j}} + 7\hat{\text{k}}$ and a vector $\bar{\text{m}}$ is such that $\bar{\text{m}} \times \bar{q} = \bar{r} \times \bar{q}, \bar{\text{m}} \cdot \bar{p} = 0$, then $\bar{\text{m}} = .......$

If \( p \to (\sim p \lor q) \) is false, then the truth values of \( p \) and \( q \) are, respectively

The logical statement \((p \to q) \land (q \to \sim p)\) is equivalent to

Negation of $(p \land q) \rightarrow (\sim p \lor r)$ is

p : It rains today
q : I am going to school
r : I will meet my friend
s : I will go to watch a movie.
Then symbolic form of the statement "If it does not rain today or I won't go to school, then I will meet my friend and I will go to watch a movie" is

The logical expression $p \wedge(\sim p \vee \sim q) \equiv$

The negation of a statement '$x \in A \cap B \rightarrow (x \in A \text{ and } x \in B)$' is

If $p, q$ are true statements and $r$ is false statement, then which of the following is correct.

Negation of the statement $\forall x \in R, x^2+1=0$ is