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# Lecture - 4 Chapter 1 Sets

Don’t let the fear of losing be greater than the excitement of winning. – Robert Kiyosaki

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NCERT EXERCISE 1.5 |

- Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9} , A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }. Find

*(i)*A′*(ii)*B′- (A ∪ C)′
- (A ∪ B)′
*(v)*(A′)′- (B – C)′

- If U = {
*a*,*b*,*c*,*d*,*e*,*f*,*g*,*h*}, find the complements of the following sets:

*(i)*A = {*a*,*b*,*c*}*(ii)*B = {*d*,*e*,*f*,*g*}

- C = {
*a*,*c*,*e*,*g*} - D = {
*f*,*g*,*h*,*a*}

- Taking the set of natural numbers as the universal set, write down the complements of the following sets:

- {
*x*:*x*is an even natural number} - {
*x*:*x*is an odd natural number } - {
*x*:*x*is a positive multiple of 3} - {
*x*:*x*is a prime number } - {
*x*:*x*is a natural number divisible by 3 and 5} - {
*x*:*x*is a perfect square } - {
*x*:*x*is a perfect cube} - {
*x*:*x*+ 5 = 8 } - {
*x*: 2*x*+ 5 = 9} - {
*x*:*x*≥ 7 } - {
*x*:*x*∈ N and 2*x*+ 1 > 10 }

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##### Clip - 1

- If U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = {2, 4, 6, 8} and B = { 2, 3, 5, 7}. Verify that

*(i)*(A ∪ B)′ = A′ ∩ B′*(ii)*(A ∩ B)′ = A′ ∪ B′

- Draw appropriate Venn diagram for each of the following:

*(i)*(A ∪ B)′,*(ii)*A′ ∩ B′,

(A ∩ B)′,

- A′ ∪ B′

- Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A′?

- Fill in the blanks to make each of the following a true statement:

*(i)*A ∪ A′ = . . .*(ii)*f′ ∩ A = . . .- A ∩ A′ = . . .
- U′ ∩ A = . . .

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