Cardinal Properties

Q.

Consider the following statements.

I. If $A_n$ is the set of first $n$ prime numbers, Then $\underset{n=2}{\overset{10}{\cup }}{A}_n$ is equal to $\{2,3,5,7,11,13,17,19,23,29\}$

II. If $A$ and $B$ are two sets such that $n(A\cup B)=50,n\left(A\right)=28,n\left(B\right)=32,$ then $n(A\cap B)=10.$

Which of these is correct?

1. Only I is true.

2. Only II is true.

3. Both are true.

4. Both are false.

Q. Verify n(A $\cup$ B $\cup$ C) = n(A) + n(B) + n(C) – n(A $\cap$ B) – n(B $\cap$ C) – n(A $\cap$ C) + n(A $\cap$ B $\cup$ C) for the following sets. A = {a, c, e, f, h}, B = {c, d, e, f} and C = {a, b, c, f}

Q.

A and B are finite sets such that n(A) = 17 and n(B) = 29. If A is a subset of B, then, $n\left(\right(A\cup B)-(A\cap B\left)\right)$= ___ .

Q.

A survey shows that 63% of the people watch news whereas 76% watch sports. If $x$% of people watch both sports and news, then

1. $x=63$

2. $x=39$

3. $39\le x\le 63$

4. $0\le x\le 39$

Q.

A survey shows that 63% of the people watch news whereas 76% watch sports. If $x$% of people watch both sports and news, then

1. $x=39$

2. $x=63$

3. $39\le x\le 63$

4. $0\le x\le 39$

Q.

$(A-B)\cap (C-B)=$

1. $(A-C)\cap B$

2. $B-(A\cap C)$

3. $(A\cap C)-B$

4. $A\cap B\cap C$

Q. A student on his birthday distributed on an average $5$ chocolates per student. If on the arrival of the teacher and the headmaster to whom the student gives $10$ and $15$ chocolates respectively, the average chocolate distributed per head increases to $5.5$, then what is the number of students in the class?

1. $28$
2. $30$
3. $32$
4. $36$

Q.

A and B are finite sets such that n(A)=17 and n(B)=29. If A is a subset of B, then, $n\left(\right(A\cup B)-(A\cap B\left)\right)$= ___ .

Q. Verify n (A $\cup$ B $\cup$ C) = n (A) + n(B) + n (C) – n(A $\cap$ B) – (B $\cap$ C) – n(A $\cap$ C) + (A $\cap$ B $\cup$ C) for the following sets A = {1, 3, 5, 6, 8}, B = {3, 4, 5, 6} and C = {1, 2, 3, 6}

Q. In a certain state, $5261989$ students were enrolled in various schools. Of these, $1965233$ students enrolled in primary school, $2006756$ students enrolled in high school and the rest in middle school. How many students enrolled in middle school?

1. $1290000$
2. $2005233$
3. $1966756$
4. $219000$

Q. Prove that $A-(A-B)=A\cap B$

Q.

If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B ={2, 4, ......, 18} and N, the set of natural numbers is the universal set, then $(A^{\prime }\cup [(A\cup B)\cap B^{\prime }\left]\right)$ is

1. $\varphi$

2. A

3. B

4. N

Q.

$(A-B)\cap (C-B)=$

1. $(A-C)\cap B$

2. $B-(A\cap C)$

3. $(A\cap C)-B$

4. $A\cap B\cap C$

Q. If $R$ = {1, 3, 5, 7, 9, 11, 13}, then which of the following is not a subset of $R$ ?

1. {1, 9, 5, 13}
2. {5, 11, 1}
3. {0}
4. {}