Or

Q. The proposition $\sim (p\vee \sim q)\vee \sim (p\vee q)$ is logically equivalent to

1. $q$
2. $\sim p$
3. $\sim q$
4. $p$

Q. The disjunction of the statement, "Hyderabad is in India", "$2+2=4$" is

1. Hyderabad is in India and $2+2=4.$
2. Hyderabad is in India but not $2+2=4.$
3. Hyderabad is not in India or $2+2=4.$
4. Hyderabad is in India or $2+2=4.$

Q.

Find:

$25-(-13)$

Q. The disjunction of the statements,
"$1+2=3$", "$3+4=6$" is

1. neither $1+2=3$ nor $3+4=6.$
2. $1+2=3$ and $3+4=6.$
3. $1+2=3$ or $3+4=6.$
4. $1+2=3$ but not $3+4=6.$

Q. Which among the following statements are connected by logical connective 'exclusive OR'
$A:$ An integer greater than $1$ is prime or composite
$B:$ sun rises or moon rises
$C:$ You can go through steps or lift

1. $A$ and $C$
2. $B$ and $C$
3. $A$ and $B$
4. $A,B$ and $C$

Q. Which among the following statements are connected by logical connective 'inclusive OR'
$P:14$ is an even or rational number
$Q:\sqrt{3}$ is a rational or irrational number
$R:$ To enter the hospital you should be doctor or you need to submit covid $19$ negative certificate.

1. $P$ and $R$
2. $P$ and $Q$
3. All
4. $Q$ and $R$

Q.

What is the negation of the statement 3 + 7 = 10

1. 3 + 7 $\ne$ 10

2. 10 = 3 + 7

3. 3 + 7$>$ 10

4. 3 + 7 = -10

Q. The disjunction of the statements, "Hyderabad is in India", "$2+2=4$" is

1. Hyderabad is in India and $2+2=4.$
2. Hyderabad is in India or $2+2=4.$
3. Hyderabad is in India but not $2+2=4.$
4. Hyderabad is not in India or $2+2=4.$

Q.

Let $P,Q,R$ be three points on the ellipse $x^2+4y^2=4$ and $P^{\prime },Q^{\prime },R^{\prime }$ be the corresponding points on the auxiliary circle. Then Area of $△P^{\prime }{Q}^{\prime }{R}^{\prime }$ $:$ Area of $△PQR$ is

Q. If $ab+4=cd$ and $ba+40=dc$, where $ab,cd,ba$ and $dc$ are $2$ digit prime numbers. Further $b$ and $d$ are the prime numbers and $a,c$ are neither prime nor composite. Find the value of $\frac{ab+ba}{cd+dc}$.

Q.

Consider the statement $S:"0\times 0=81\text{OR}1\times 1=81\text{OR}2\times 2=81\text{OR}3\times 3=81$, and so on”. S is strictly a logical disjunction

1. True

2. False

Q.

State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer.

(i) Sun rises or Moon sets.

(ii) To apply for a driving licence, you should have a ration card or a passport.

(iii) All integers are positive or negative.

Q.

Subtract $-27$from $75$.

Q. Subtract:
$\left(vi\right)-xy+yz-zx$ from $xy-yz+xz$

Q.

For any rational number $x$, $x+(-1)=-x$. State whether the statement is true (T) or false (F).

1. True
2. False

Q. If $3p^2=5p+2$ and $3q^2=5q+2$, where $p\ne q$, then $pq$ is equal to

1. $\frac{2}{3}$
2. $-\frac{2}{3}$
3. $\frac{3}{2}$
4. $-\frac{3}{2}$

Q.

For each of the following statements, determine whether an inclusive "OR" or exclusive "OR" is used. Give reasons for your answer.

(i) Students can take Hindi or sanskrit as their third language.

(ii) To entry a country, you need a passport or a voter registration card.

(iii) A lady gives birth to a baby boy or a baby girl.

(iv) To apply for a driving licence, you should have a ration card or a passport.

Q. Change the sentences into passive voice
1)The assistant handed me a note.
2)Someone has taken my wallet.
3) Many people used bicycle as a means of transport.
4)They advised me to get a visa.

Q. Let $A=\{p,q,r,s\}$ and $B=\{1,2,3\}$. Which of the following relations from $A$ to $B$ is not a function?

1. $R_1=\left\{\right(p,1),(p,2),(r,1),(s,2\left)\right\}$
2. $R_3=\left\{\right(p,1),(q,2),(r,2),(r,2\left)\right\}$
3. $R_2=\left\{\right(p,1),(q,2),(r,1),(s,1\left)\right\}$
4. $R_4=\left\{\right(p,2),(q,3),(r,2),(s,2\left)\right\}$

Q. Let $p\left(x\right)=a{x}^2+bx+c,q\left(x\right)=l{x}^2+mx+n.$ If $p\left(1\right)-q\left(1\right)=0$, $p\left(2\right)-q\left(2\right)=1$ and $p\left(3\right)-q\left(3\right)=4$, then $p\left(4\right)-q\left(4\right)$ equals

1. $0$
2. $5$
3. $6$
4. $9$

Q. Events $A$ and $B$ are such that $P\left(A\right)=\frac{1}{2},P\left(B\right)=\frac{7}{12}$ and $P\left(notAornotB\right)=\frac{1}{4}$. State whether $A$ and $B$ are independent ?

1. True
2. False

Q. Which of the following is(are) incorrect for the statement $p$ and $q$ ?

1. $p\wedge q$ is true when atleast one from $p$ and $q$ is true.
2. $p\to q$ is true when $p$ is true and $q$ is false.
3. $p\leftrightarrow q$ is true only when both $p$ and $q$ are true.
4. None of these.

Q. If one G.M. '$G$' and two arithmetic means $p$ and $q$ be inserted between any two given number then $G^2=$

1. $(2p-q)(2q-p)$
2. $(2p-q)(q-2p)$
3. $\frac{2p+q}{q+2p}$
4. $\frac{2p+q}{2q+p}$

Q. If Q (3, 1) is equidistant from P ( 5, -3) and R ( x 6), then positive value of x is

1. 5
2. 4
3. 2
4. none of the above

Q. Write the dual of the following.
$(\sim p\vee q)\wedge (\sim r\wedge s)$