Union

Q. Let U = {0, 1, 2 , 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3, 5, 7}, find the following sets.

(i) A’
(ii) B’
(iii) A ‘ $\cup$ B’
(iv) A’ $\cap$ B’
(v) (A $\cup$ B)’
(vi) (A $\cap$ B)’
(vii) (A’)’
(viii) (B’)’

Q.

Q. 63.The product of the first n odd natural numbers equals?

Q.

Q. Express $44$ as the sum of two odd primes.

Q. What is the units' digit of the product of all prime numbers between $1$ and $100$?

1. $0$
2. $2$
3. $1$
4. $3$

Q. Number of prime numbers between $50$ to $60$ is:

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

Q. State which of the following sets are equal.
(i) N = {1, 2, 3, 4, ....}
(ii) W = {0, 1, 2, 3, ...}
(iii) A = {x|x = 2ⁿ, n $\in$ W}
(iv) B = W $-$ {0}

Q. If A = {5, 6, 7, 8} and B = {7, 8, 9, 11}, then find A ∪ B.

Q.

Suppose $A_1,A_2,.....................A_{3}0$ are thirty sets each having 5 elements and $B_1,B_2,................B_n$ are n sets each with 3 elements, let $\bigcup _{i=1}^{30}$$A_i$=$\bigcup _{j=1}^n$$B_j=S$ and each element of S belongs to exactly 10 of $A_i$'S and exactly 9 of the $B_j$'S. Then $n$ is equal to

1. 15

2. 3

3. 45

4. 50

Q. The union of two sets A and B contain elements which are present in A ___ B.

1. and
2. or
3. less than
4. greater than

Q. If A = {5, 6, 7, 8} and B = {7, 8, 9, 11}, then find A ∪ B.

Q. The number of elements in the set {(a, b) : 2a^2 + 3b^2 = 35. a . b in Z}, where Z is the set of all integers, is

Q. If A = {-3, -2, 1, 4} and B = {0, 1, 2, 4}, find (i) A – B (ii) B – A.

Q. If $f\left(x\right)={\int }_a^x\left[f\right(x){]}^{-1}dx$ and ${\int }_a^1\left[f\right(x){]}^{-1}dx=\sqrt{2},$ then

1. $f\left(2\right)=2$
2. $f^{-1}\left(2\right)=2$
3. ${\int }_0^{1}f\left(x\right)dx=\sqrt{2}$
4. $f^{\prime }\left(2\right)=1/2$

Q. Different between power set and subset

Q. Write set builder form: 30 less then whole number