If A = { 4 , 5 , 7 , 8 , 10 } , B = { 4 , 5 , 9 } and C = { 1 , 4 , 6 , 9 } , verified that A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C ) .

To verify, A ∪ ( B ∩ C ) = ( A ∪ B ) ∩ ( A ∪ C ) L H S = A ∪ ( B ∩ C ) = { 4 , 5 , 7 , 8 , 10 } ∪ { 4 , 5 , 9 } ∩ { 1 , 4 , 6 , 9 } = { 4 , 5 , 7 , 8 , 10 } ∪ { 4 , 9 } = { 4 , 5 , 7 , 8 , 9 , 10 } R H S = A ∪ B ∩ ( A ∪ C ) = { 4 , 5 , 7 , 8 , 10 } ∪ { 4 , 5 , 9 } ∩ { 4 , 5 , 7 , 8 , 10 } ∪ { 1 , 4 , 6 , 9 } = { 4 , 5 , 7 , 8 , 9 , 10 } ∩ { 1 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } = { 4 , 5 , 7 , 8 , 9 , 10 } Hence, RHS = LHS

For any two set A and B , prove that ( A ∪ B ) ' = A ' ∩ B ' .

Let x be an arbitrary element of ( A ∪ B ) ' . Then, x ∈ ( A ∪ B ) ' ⇒ x ∉ ( A ∪ B ) ⇒ x ∉ A and x ∉ B ⇒ x ∈ A ' and x ∈ B ' ⇒ x ∈ A ' ∩ B ' ∴ ( A ∪ B ) ' ⊆ A ' ∩ B ' Again, let y be an arbitrary element of A ' ∩ B ' . Then y ∈ A ' ∩ B ' ⇒ y ∈ A ' and y ∈ B ' ⇒ y ∉ A and y ∉ B ⇒ y ∉ A ∪ B ⇒ y ∈ ( A ∪ B ) ' ∴ A ' ∩ B ' ⊆ ( A ∪ B ) ' Hence, ( A ∪ B ) ' = A ' ∩ B '

E M B I B E

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST

A P Prabhakaran Solutions for Chapter: Sets, Exercise 1: SELF EVALUATION TEST

Author:A P Prabhakaran

A P Prabhakaran Mathematics Solutions for Exercise - A P Prabhakaran Solutions for Chapter: Sets, Exercise 1: SELF EVALUATION TEST

Attempt the free practice questions on Chapter 1: Sets, Exercise 1: SELF EVALUATION TEST with hints and solutions to strengthen your understanding. Golden MATHEMATICS CLASS 11 solutions are prepared by Experienced Embibe Experts.

Questions from A P Prabhakaran Solutions for Chapter: Sets, Exercise 1: SELF EVALUATION TEST with Hints & Solutions

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 2

Write the set $\{x : x is prime and 10 < x < 30\}$ in roster form.

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 5

If $A = \{a, b, c\}$ write the power set of $A$

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 6

If $A = {4, 5, 7, 8, 10}, B = {4, 5, 9}$ and $C = {1, 4, 6, 9}$ , verified that $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$ .

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 7

If $A = {4, 5, 8, 12}, B = {1, 4, 6, 9}$ and $C = {1, 2, 4, 7, 8}$ then find $A - (B - C)$ .

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 7

If $A = \{4, 5, 8, 12\}, B = {1, 4, 6, 9}$ and $C = {1, 2, 4, 7, 8}$ then find $A - (B \cap C)$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 8

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the subsets of second set. Find the values of $m, n$ .

HARD

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 9

In a group of $20$ students, $12$ take tea, $16$ take coffee and $3$ take neither of the two. How many take both tea and coffee?

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 1 - Sets>SELF EVALUATION TEST>Q 10

For any two set $A$ and $B$ , prove that $(A \cup B)^{'} = A^{'} \cap B^{'}$ .