If U = { x / x ∈ N , 1 ≤ x ≤ 12 } A = { 1 , 4 , 7 , 10 } B = { 2 , 4 , 6 , 7 , 11 } C = { 3 , 5 , 8 , 9 , 12 } Write down the set A ∪ B

Given that U = { x / x ∈ N , 1 ≤ x ≤ 12 } ∴ U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } A = { 1 , 4 , 7 , 10 } , B = { 2 , 4 , 6 , 7 , 11 } , C = { 3 , 5 , 8 , 9 , 12 } We know that the union of sets A and B is the set which consists of all the elements of A and all the elements of B , and the common elements of set A and B being taken only once. ∴ A ∪ B = { 1 , 2 , 4 , 6 , 7 , 10 , 11 } .

If U = { x / x ∈ N , 1 ≤ x ≤ 12 } A = { 1 , 4 , 7 , 10 } B = { 2 , 4 , 6 , 7 , 11 } C = { 3 , 5 , 8 , 9 , 12 } Write down the set B ∩ C

Given that U = { x / x ∈ N , 1 ≤ x ≤ 12 } ∴ U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } A = { 1 , 4 , 7 , 10 } , B = { 2 , 4 , 6 , 7 , 11 } , C = { 3 , 5 , 8 , 9 , 12 } The intersection of sets B and C is the set of all elements which are common to both B and C . B ∩ C = { 2 , 4 , 6 , 7 , 11 } ∩ { 3 , 5 , 8 , 9 , 12 } Since there is no element common in sets B and C . ∴ B ∩ C = { }

If U = { x / x ∈ N , 1 ≤ x ≤ 12 } A = { 1 , 4 , 7 , 10 } B = { 2 , 4 , 6 , 7 , 11 } C = { 3 , 5 , 8 , 9 , 12 } Write down the set A - B

Given that U = { x / x ∈ N , 1 ≤ x ≤ 12 } ∴ U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } A = { 1 , 4 , 7 , 10 } , B = { 2 , 4 , 6 , 7 , 11 } , C = { 3 , 5 , 8 , 9 , 12 } The difference of the sets A and B in this order is the set of elements which belong to A but not to B . A - B = { 1 , 4 , 7 , 10 } - { 2 , 4 , 6 , 7 , 11 } ∴ A - B = { 1 , 10 }

If U = { x / x ∈ N , 1 ≤ x ≤ 12 } A = { 1 , 4 , 7 , 10 } B = { 2 , 4 , 6 , 7 , 11 } C = { 3 , 5 , 8 , 9 , 12 } Write down the set B ∩ C '

Given that U = { x / x ∈ N , 1 ≤ x ≤ 12 } = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } A = { 1 , 4 , 7 , 10 } , B = { 2 , 4 , 6 , 7 , 11 } , C = { 3 , 5 , 8 , 9 , 12 } Since U is universal set and C is subset of U . So, the complement of C is the set of all elements of U which are not the elements of C . i.e., C ' = { 1 , 2 , 4 , 6 , 7 , 10 , 11 } The intersection of two sets is the set of all those elements which belong to both the sets. ∴ B ∩ C ' = { 2 , 4 , 6 , 7 , 11 } ∩ { 1 , 2 , 4 , 6 , 7 , 10 , 11 } = { 2 , 4 , 6 , 7 , 11 }

If U = { x / x ∈ N , 1 ≤ x ≤ 12 } A = { 1 , 4 , 7 , 10 } , B = { 2 , 4 , 6 , 7 , 11 } C = { 3 , 5 , 8 , 9 , 12 } Write down the set A ∪ B ∪ C

Given that U = { x / x ∈ N , 1 ≤ x ≤ 12 } ∴ U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } A = { 1 , 4 , 7 , 10 } , B = { 2 , 4 , 6 , 7 , 11 } , C = { 3 , 5 , 8 , 9 , 12 } if A , B , and C are three sets, their union is a set containing all elements that are in at least one of the sets. A ∪ B ∪ C = { 1 , 4 , 7 , 10 } ∪ { 2 , 4 , 6 , 7 , 11 } ∪ { 3 , 5 , 8 , 9 , 12 } ∴ A ∪ B ∪ C = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

If U = { x / x ∈ N , 1 ≤ x ≤ 12 } A = { 1 , 4 , 7 , 10 } B = { 2 , 4 , 6 , 7 , 11 } C = { 3 , 5 , 8 , 9 , 12 } Write down the set A ∩ B ∪ C

Given that U = { x / x ∈ N , 1 ≤ x ≤ 12 } = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } A = { 1 , 4 , 7 , 10 } , B = { 2 , 4 , 6 , 7 , 11 } , C = { 3 , 5 , 8 , 9 , 12 } We know that the union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both). B ∪ C = { 2 , 4 , 6 , 7 , 11 } ∪ { 3 , 5 , 8 , 9 , 12 } ∴ B ∪ C = { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 11 , 12 } The intersection of sets A and B is the set of all elements which are common to both A and B . ∴ A ∩ ( B ∪ C ) = { 1 , 4 , 7 , 10 } ∩ { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 11 , 12 } = { 4 , 7 } Hence, A ∩ ( B ∪ C ) = 4 , 7 .

E M B I B E

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE

Maharashtra Board Solutions for Chapter: Sets and Relations, Exercise 3: MISCELLANEOUS EXERCISE

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Sets and Relations, Exercise 3: MISCELLANEOUS EXERCISE

Attempt the practice questions on Chapter 5: Sets and Relations, Exercise 3: MISCELLANEOUS EXERCISE with hints and solutions to strengthen your understanding. Mathematics and Statistics (Arts & Science) Part 2 solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Sets and Relations, Exercise 3: MISCELLANEOUS EXERCISE with Hints & Solutions

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

If $U = {x / x \in N, 1 \leq x \leq 12}$

$A = {1, 4, 7, 10} B = {2, 4, 6, 7, 11}$

$C = {3, 5, 8, 9, 12}$

Write down the set

$A \cup B$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

If $U = {x / x \in N, 1 \leq x \leq 12}$

$A = {1, 4, 7, 10} B = {2, 4, 6, 7, 11}$

$C = {3, 5, 8, 9, 12}$

Write down the set

$B \cap C$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

If $U = {x / x \in N, 1 \leq x \leq 12}$

$A = {1, 4, 7, 10} B = {2, 4, 6, 7, 11}$

$C = {3, 5, 8, 9, 12}$

Write down the set

$A - B$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

If $U = {x / x \in N, 1 \leq x \leq 12}$

$A = {1, 4, 7, 10} B = {2, 4, 6, 7, 11}$

$C = {3, 5, 8, 9, 12}$

Write down the set

$B \cap C^{'}$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

If $U = {x / x \in N, 1 \leq x \leq 12}$

$A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}$

$C = {3, 5, 8, 9, 12}$

Write down the set
$A \cup B \cup C$

EASY

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

If $U = {x / x \in N, 1 \leq x \leq 12}$

$A = {1, 4, 7, 10} B = {2, 4, 6, 7, 11}$

$C = {3, 5, 8, 9, 12}$

Write down the set

$A \cap (B \cup C)$

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

In a survey of $425$ students in a school, it was found that $115$ drink apple juice, $160$ drink orange juice and $80$ drink both apple as well as orange juice. How many drink neither apple juice nor orange juice?

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 2>Chapter 5 - Sets and Relations>MISCELLANEOUS EXERCISE>Q (II)

In a school there are $20$ teachers who teach Mathematics or Physics. Of these, $12$ teach Mathematics and $4$ teach both Physics and Mathematics. How many teachers teach Physics?

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