Question

2. A ∪ A
'= ………….

(a) A (b) A′ (c) ∪ (d) ∅

3. If n(A) = 7, n(B) = 13, n(A ∪ B) = 16, then find n(A ∩ B) = ?

(a) 6 (b) 8 (c) ∅ (d) 4

4. The set of odd positive integers less than 10 cm be expressed by ……………. .

(a) {1, 2, 3} (b) {1, 2, 5, 9} (c) {1, 5, 7, 9, 11} (d) {1, 3, 5, 7, 9}

5. A set of all even prime numbers ……………. .

(a) {2, 4, 6……} (b) {2, 3, 5……} (c) { 2 } (d) ∅​

Answer 1

2.

The union of a set with itself is equal to the set itself. This is known as idempotent law.

$\displaystyle\longrightarrow\sf{\underline {\underline {A\cup A=A}}}$

3.

We have the formula,

$\displaystyle\longrightarrow\sf{n(A\cap B)=n(A)+n(B)-n(A\cup B)}$

Here,

• $\displaystyle\sf {n(A)=7}$

• $\displaystyle\sf {n(B)=13}$

• $\displaystyle\sf {n(A\cup B)=16}$

Then,

$\displaystyle\longrightarrow\sf{n(A\cap B)=7+13-16}$

$\displaystyle\longrightarrow\underline {\underline {\sf{n(A\cap B)=4}}}$

4.

Odd positive integers less than 10 are 1, 3, 5, 7 and 9.

Hence the set is $\displaystyle\sf {\{1,\ 3,\ 5,\ 7,\ 9\}.}$

5.

There is only one even prime number, i.e., 2.

Hence the set is $\displaystyle\sf {\{2\}.}$