Mathematical Reasoning

Number of switches in alternative equivalent simple circuit for the circuit is (are)

Consider the statements given by following
(A) If $4+3=8$, then $5+3=9$
(B) If $6+4=10$, then moon is flat
(C) If both (A) and (B) are true, then $5+6=17$
Then which of the following statement is correct?

If the truth value of the statement pattern $[p \wedge \sim r] \rightarrow \sim r \wedge q$ is False, then which of the following has truth value False?

Which of the following statements has the truth value T ?
A: cube roots of unity are in Geometric progression and their sum is 1
B: $4+7>10$ iff $2+8<10$
C: $\exists x \in \mathbb{N}$ such that $x^2-3 x+2=0$ and $\exists \mathrm{n} \in \mat...

If $p$ : switch $S_1$ is closed, $q$ : switch $S_2$ is closed, $r$ : switch $S_3$ closed, then the symbolic form of the following switching circuit is equivalent to
Switching Circuit:

$p:$ If 7 is an odd number then 7 is divisible by 2 .
q : If 7 is prime number then 7 is an odd number. If $V_1$ and $V_2$ are respective truth values of contrapositive of p and q then $\left(\mathrm{V}_1, \mathrm{~V}_2\right) \equiv$

If the statement pattern $(p \wedge q) \rightarrow(r \vee \sim s)$ is false, then the truth values of $p, q, r$ and $s$ are respectively

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

The correct simplified circuit diagram for the logical statement $[\{\mathrm{q} \wedge(\sim \mathrm{q} \vee \mathrm{r})\} \wedge\{\sim \mathrm{p} \vee(\mathrm{p} \wedge \sim \mathrm{r})\}] \vee(\mathrm{p} \wedge \mathrm{r})$ Where $p, q, r$...

If $\{(\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\mathrm{p} \wedge \mathrm{r})\} \rightarrow \sim \mathrm{p} \vee \mathrm{q}$ has truth value false then truth values of the statements $p, q, r$ are respectively

The logically equivalent statement of $(\sim \mathrm{p} \wedge \mathrm{q}) \vee(\sim \mathrm{p} \wedge \sim \mathrm{q}) \vee(\mathrm{p} \wedge \sim \mathrm{q})$ is

If a statement $q$ has truth value False and $(\mathrm{p} \wedge \mathrm{q}) \leftrightarrow \mathrm{r}$ has truth value True then which of the following has truth value true?

The equivalent statement of "If three vertices of a triangle are represented by cube roots of unity, then the triangle is an equilateral triangle" is

The negation of $(p \wedge \sim q) \rightarrow(p \vee \sim q)$ is

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

Consider the three statements $\mathrm{p}: \forall \mathrm{n} \in \mathbb{N}, 10 \mathrm{n}-3$ is a prime number, when n is not divisible by 3.
$\mathrm{q}: \frac{2}{\sqrt{3}}, \frac{-2}{\sqrt{3}}, \frac{-1}{\sqrt{3}}$ are the direction cos...

Which of the following are pairs of equivalent circuits

The last column in the truth table of the statement pattern $[\mathrm{p} \rightarrow(\mathrm{q} \wedge \sim \mathrm{p})] \vee[(\mathrm{p} \vee \sim \mathrm{q}) \wedge \mathrm{p}]$ is

Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively

Consider the statements given by following :
(A) If $3+3=7$, then $4+3=8$.
(B) If $5+3=8$, then earth is flat.

(C) If both (A) and (B) are true, then $5+6=17$.
Then which of the following statements is correct?

If $\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \sim \mathrm{q})$ is false, then the truth values of p and q are respectively

Negation of the statement ' Horses have wings if and only if crows have tails. ' is

If $(p \wedge \sim q) \wedge(p \wedge r) \rightarrow \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are respectively

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

If the statements $p, q$ and $r$ have the truth values $\mathrm{F}, \mathrm{T}, \mathrm{F}$ respectively, then the truth values of the statement patterns $(p \wedge \sim q) \rightarrow r$ and $(p \vee q) \rightarrow r$ are respectively

The converse of $[p \wedge(\sim q)] \rightarrow r$ is

Consider the following statements
p : the switch $\mathrm{S}_1$ is closed.
q : the switch $\mathrm{S}_2$ is closed.
$r$ : the switch $\mathrm{S}_3$ is closed.
Then the switching circuit represented by the statement $(p \wedge q) \vee(\sim p...

If p and q are statements, then _________ is a contingency.

The new switching circuit for the following circuit by simplifying the given circuit is

\(\sim[(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow(\mathrm{p} \wedge \sim \mathrm{q})] \equiv\)

If statement I : If the work is not finished on time, the contractor is in trouble.
statement II : Either the work is finished on time or the contractor is in trouble.
then

If the statement $p \vee \sim(q \wedge r)$ is false, then the truth values of $p, q$ and $r$ are respectively

Which one of the following is the pair of equivalent circuits?

The negation of contrapositive of the statement $\mathrm{p} \rightarrow(\sim \mathrm{q} \wedge \mathrm{r})$ is

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

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:
p : There is a rational number $x \in \mathrm{~S}$ such that $x>0$.
Which of the following statements is the negation of the statement p?

The statement $\sim(p \leftrightarrow \sim q)$ is

Truth values of $\mathrm{p} \rightarrow \mathrm{r}$ is F and $\mathrm{p} \leftrightarrow \mathrm{q}$ is F . Then the truth values of $(\sim p \vee q) \rightarrow(p \vee \sim q)$ and $(p \wedge \sim q) \rightarrow(\sim p \wedge q)$ are respe...

Contrapositive of the statement. 'If two numbers are equal, then their squares are equal' is

If $p \rightarrow(q \vee r)$ is false, then the truth values of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are respectively

If p : The total prime numbers between 2 to 100 are 26.
q : Zero is a complex number.
$r$ : Least common multiple (L.C.M.) of 6 and 7 is 6 .
Then which of the following is correct?

The contrapositive of the inverse of $\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is

Let $\mathrm{p}, \mathrm{q}$ and r be the statements
$\mathrm{p}: \mathrm{X}$ is an equilateral triangle
$\mathrm{q}: \mathrm{X}$ is isosceles triangle
r: q $\vee \sim p$,
then the equivalent statement of $r$ is

Let p : A man is judge.
$\mathrm{q}: \mathrm{He}$ is honest.
The inverse of $p \rightarrow q$ is

The following statement $(\mathrm{p} \rightarrow \mathrm{q}) \rightarrow((\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow \mathrm{q})$ is

Contrapositive of the statement
'If two numbers are not equal, then their squares are not equal', is

The inverse of $p \rightarrow(q \rightarrow r)$ is logically equivalent to

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

If $(p \wedge \sim r) \rightarrow(\sim p \vee q)$ has truth value False, then truth values of $p, q, r$ are respectively.

The converse of "If 3 is a prime number, then 3 is odd." is