Fallacy

Q. The number of choices for $\Delta \in \{\wedge ,\vee ,\Rightarrow ,\iff \}$, such that $\left(p\Delta q\right)\Rightarrow \left(\right(p\Delta \sim q)\vee ((\sim p)\Delta q\left)\right)$ is a tautology, is

1. $2$
2. $3$
3. $1$
4. $4$

Q. Consider a tangent to the ellipse $\frac{x^2}{2}+\frac{y^2}{1}=1$ at any point. The locus of the midpoint of the portion intercepted between the axes is

1. $\frac{x^2}{2}+\frac{y^2}{4}=1$
2. $\frac{x^2}{4}+\frac{y^2}{2}=1$
3. $\frac{1}{3x^2}+\frac{1}{4y^2}=1$
4. $\frac{1}{2x^2}+\frac{1}{4y^2}=1$

Q. If the truth value of the statement $(P\wedge (\sim R\left)\right)\to \left(\right(\sim R)\wedge Q)\text{is}F$, then the truth value of which of the following is $F$?

Q. Let $r\in \{p,q,\sim p,\sim q\}$ be such that the logical statement $r\vee (\sim p)\Rightarrow (p\wedge q)\vee r$ is a tautology. Then $r$ is equal to :

Q. The logical statement $(p\to \sim q)\leftrightarrow (p\wedge q)$ is

1. a tautology
2. a contradiction
3. neither a tautology nor a contradiction
4. equivalent to $\sim p\vee q$

Q. The proposition $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is

1. Tautology and contradiction
2. Neither tautology nor contradiction
3. Contradiction
4. Tautology

Q.

Convert the following equations in statement forms

$x-5=9$

Q. Choose the option that best describes the meaning of the idiom/phrase underlined in the given sentence.

He let the grass grow under his feet.

1. Inactive
2. Mobile
3. Nature lover
4. Curious

Q. Arun rides his bicycle from house at A to club C via B taking the shortest path. Then the shortest path that he can choose is .
Options
A)1170 B)630 C)792 D)1200. E)936
I am in need of ur answer and explaination for the soon.
Thank you!.

Q.

What is square of $7$?

Q. $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is

1. A tautology
2. Both a tautology and a contradiction
3. A contradiction
4. Neither a tautology nor a contradiction

Q. Consider
Statement I: $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.
Statement II: $(p\to q)\leftrightarrow (\sim q\to \sim p)$ is a tautology.

1. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

2. Statement I is true; Statement II is false

3. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
4. Statement I is false; Statement II is true

Q. Let
$p:57$ is an odd prime number
$q:4$ is a divisor of $12$
$r:15$ is the LCM of $3$ and $5$
be three simple logical statements. Which one of the following is true?

1. $(p\vee (q\wedge r)$
2. $(p\vee q)\wedge r$
3. $p\vee (\sim q\wedge r)$
4. $\sim p\vee (q\wedge r)$
5. $(p\wedge q)\vee \sim r$

Q. State true or false.

1. True
2. False

Q. State whether the following statements are true or false. Give reasons for your answers.
For any real number $x,x^2\ge 0$.

1. True
2. False

Q.

Can there exist a set of numbers which does not contain real numbers? If yes, how do we represent it .

Q. Verify the property $a\times (b+c)=(a\times b)+(a\times c)$ When $a=\frac{1}{2},b=\frac{3}{7}\&c=\frac{5}{14}$.

Q. Which of the following is not proposition?

1. $3$ is prime.
2. $\sqrt{2}$ is irrational.
3. $5$ is an even integer.
4. Mathematics is interesting.

Q. Which one of the following statements is not a false statement?

1. $q:$ Circle is a particular case of an ellipse.
2. $p:$ Each radius of a circle is a chord of the circle.
3. $r:\sqrt{13}$ is a rational number.
4. $s:$ The centre of a circle bisects each chord of the cirlce.

Q. Choose the option that best describes the meaning of the idiom/phrase underlined in the given sentence.

We should bury the hatchet and become friends.

1. obtain
2. influence friends
3. make peace
4. keep a secret

Q. Consider
Statement I: $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.
Statement II: $(p\to q)\leftrightarrow (\sim q\to \sim p)$ is a tautology.

1. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
2. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I

3. Statement I is true; Statement II is false

4. Statement I is false; Statement II is true

Q. Find the total surface area of a closed cylindrical petrol storage tank whose diameter 4.2 m and height 4.5 m.

Q. Assertion :STATEMENT- 1 : A straight line passing through the origin intersects the branches of the hyperbola xy = 9 at Q in the first and R in the third quadrant. The point P divides the segment QR internally in the ratio 1:2, then the locus of P is ellipse Reason: STATEMENT- 2 : $A\equiv (x_1,y_1),B\equiv (x_2,y_2)$.

1. Statement -1 is True, Statement -2 is True ; Statement -2 is a correct explanation for Statement -1
2. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-1
3. Statement -1 is True, Statement -2 is False
4. Statement -1 is False, Statement -2 is True

Q.

Let P(n) denote the statement that $n^2$ + n is odd. It

is seem that P(n) ⇒ P(n + 1), $P_n$ is true for all

1. n > 1

2. n

3. n > 2

4. None of these

Q. Prathyusha stated that "the average of first $10$ odd numbers is also $10$". Do you agree with her? Justify your answer.

Q.

The statement $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is a:

1. Fallacy

2. Neither tautology nor fallacy

3. Tautology

4. Tautology and fallacy

Q. Negation of the Boolean statement $(p\vee q)\Rightarrow \left(\right(\sim r)\vee p)$ is equivalent to

1. $(\sim p)\wedge (\sim q)\wedge r$
2. $p\wedge (\sim q)\wedge r$
3. $(\sim p)\wedge q\wedge r$
4. $p\wedge q\wedge (\sim r)$

Q. State whether the following statements are true or false. Give reasons for your answers.
Square numbers can be written as the sum of two odd numbers.

Q. Consider the following statements. The number $12375$ is
Of these statements:

1. 2 and 3 are correct
2. 1, 2 and 3 are correct
3. 1 and 3 are correct
4. 1 and 2 are correct

Q. Given are three positive integers $a,b,$ and $c$. Their greatest common divisor is $D$; their least common multiple is $M$. Then, which two of the following statements are true?
$\left(1\right)$ The product $MD$ cannot be less than $abc$
$\left(2\right)$ The product $MD$ cannot be greater than $abc$
$\left(3\right)$ $MD$ equals $abc$ if and only if $a,b,c$ are each prime
$\left(4\right)$ $MD$ equals $abc$ if and only if $a,b,c$ are relatively prime in pairs
(This means : no two have a common factor greater than $1$.)

1. $1,2$
2. $1,3$
3. $2,3$
4. $2,4$
5. $1,4$