Mathematical Reasoning

The expression $((p \wedge q) \vee(p \vee \sim q)) \wedge(\sim p \wedge \sim q)$ is equivalent to

The negation of the statement \((p \wedge q) \rightarrow(\sim p \vee r)\) is

If truth values of statements \(\mathrm{p}, \mathrm{q}\) are true, and \(\mathrm{r}\), \(s\) are false, then the truth values of the following statement patterns are respectively
$$\begin{aligned}
& \mathrm{a}: \sim(\mathrm{p} \wedge \sim \...

Let \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) be three statements, then \([p \rightarrow(q \rightarrow r)] \leftrightarrow[(p \wedge q) \rightarrow r]\) is

Negation of the statement
"The payment will be made if and only if the work is finished in time." Is

The statement \([(p \rightarrow q) \wedge \sim q] \rightarrow r\) is tautology, when \(r\) is equivalent to

The negation of the statement
"The number is an odd number if and only if it is divisible by 3."

The statement \([\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[\sim \mathrm{r} \wedge \sim \mathrm{q} \wedge \mathrm{p}]\) is equivalent to

If the statement \(\mathrm{p} \leftrightarrow(\mathrm{q} \rightarrow \mathrm{p})\) is false, then true statement/statement pattern is

Negation of inverse of the following statement pattern \((p \wedge q) \rightarrow(p \vee \sim q)\) is

The expression \((p \wedge \sim q) \vee q \vee(\sim p \wedge q)\) is equivalent to

Negation of contrapositive of statement pattern \((p \vee \sim q) \rightarrow(p \wedge \sim q)\) is

If \(q\) is false and \(p \wedge q \leftrightarrow r\) is true, then ............ is a tautology.

The contrapositive of "If \(x\) and \(y\) are integers such that \(x y\) is odd, then both \(x\) and \(y\) are odd" is

The inverse of the statement "If the surface area increase, then the pressure decreases.", is

The given following circuit is equivalent to

Let
Statement 1 : If a quadrilateral is a square, then all of its sides are equal.
Statement 2: All the sides of a quadrilateral are equal, then it is a square.

The statement pattern \(\mathrm{p} \rightarrow \sim(\mathrm{p} \wedge \sim \mathrm{q})\) is equivalent to

If truth value of logical statement \((p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)\) is false, then the truth values of \(p\) and \(q\) are respectively

The logical statement \((\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r})) \wedge(\sim \mathrm{q} \wedge \mathrm{r})\) is equivalent to

The given circuit is equivalent to

The logical statement \([\sim(\sim p \vee q) \vee(p \wedge r)] \wedge(\sim q \wedge r)\) is equivalent to

The negation of the statement pattern \(\sim s \vee(\sim r \wedge s)\) is equivalent to

If \(\mathrm{p}\) and \(\mathrm{q}\) are true statements and \(\mathrm{r}\) and \(\mathrm{s}\) are false statements, then the truth values of the statement patterns \((p \wedge q) \vee r\) and $$(\mathrm{p} \vee \mathrm{s}) \leftrightarrow(...

The negation of the statement, "The payment will be made if and only if the work is finished in time" is

If \(p: \forall n \in I N, n^2+n\) is an even number \(q: \forall n \in I N, n^2-n\) is an odd numer, then the truth values of \(p \wedge q, p \vee q\) and \(p \rightarrow q\) are respectively

The negation of the statement pattern \(p \vee(q \rightarrow \sim r)\) is

The negation of \(p \wedge(q \rightarrow r)\) is

If \(\mathrm{p}\) : It is raining and \(\mathrm{q}\) : It is pleasant, then the symbolic form of "It is neither raining nor pleasant" is

If \(\mathrm{p}\) : It is raining.
\(\mathrm{q}\) : Weather is pleasant
then simplified form of the statement "It is not true, if it is raining then weather is not pleasant" is

The negation of '\(\forall x \in N, x^2+x\) is even number' is

Negation of the statement : \(3+6>8\) and \(2+3<6\) is

S1 : If \(-\)7 is an integer, then \(\sqrt{-7}\) is a complex number
\(\mathrm{S} 2\) : \(-\)7 is not an integer or \(\sqrt{-7}\) is a complex number

"If two triangles are congruent, then their areas are equal." is the given statement, then the contrapositive of the inverse of the given statement is
(Where \(\mathrm{p}\) : Two triangles are congruent, \(\mathrm{q}\) : Their areas are equ...

The negation of inverse of \(\sim \mathrm{p} \rightarrow \mathrm{q}\) is

The expression \([(p \wedge \sim q) \vee q] \vee(\sim p \wedge q)\) is equivalent to

If statements \(\mathrm{p}\) and \(\mathrm{q}\) are true and \(\mathrm{r}\) and \(\mathrm{s}\) are false, then truth values of \(\sim(\mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{r} \wedge \mathrm{s})\) and $$(\sim \mathrm{p} ...

Let \(a: \sim(p \wedge \sim r) \vee(\sim q \vee s)\) and \(b:(p \vee s) \leftrightarrow(q \wedge r)\).
If the truth values of \(p\) and \(q\) are true and that of \(r\) and \(s\) are false, then the truth values of \(a\) and \(b\) are respe...

The statement pattern \((p \wedge q) \wedge[(p \wedge q) \vee(\sim p \wedge q)]\) is equivalent to

Given \(\mathrm{p}\) : A man is a judge, \(\mathrm{q}\) : A man is honest
If \(\mathrm{S} 1\) : If a man is a judge, then he is honest
S2 : If a man is a judge, then he is not honest
S3 : A man is not a judge or he is honest Then
S4 : A man...

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

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

The logical statement (p \(\to\) q) \(\wedge\) (q \(\to\) ~p) is equivalent to

The logical expression \(\mathrm{p} \wedge(\sim \mathrm{p} \vee \sim \mathrm{q}) \equiv\)

The negation of a statement 'x \(\in\) A \(\cap\) B \(\to\) (x \(\in\) A and x \(\in\) B)' is

Negation of \((p \wedge q) \rightarrow(\sim p \vee r)\) 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 ...

The statement pattern $p \wedge(q \vee \sim p)$ is equivalent to

The negation of the statement pattern $\sim p \vee(q \rightarrow \sim r)$ is