Given that, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } and B = { b : b ∈ U and b is a multiple of 4 } . Use Venn diagram to show A ∩ B .

Given, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } = 2 , 4 , 6 , 8 , . . . 30 , B = { b : b ∈ U and b is a multiple of 4 } = 4 , 8 , 12 , . . . 28 To find: A ∩ B We know that, A ∩ B is the set containing common elements of sets A and B . A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. Therefore, A ∩ B = 4 , 8 , 12 , 16 , 20 , 24 , 28 .

Given that, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } and B = { b : b ∈ U and b is a multiple of 4 } . Use Venn diagram to show A - B .

Given, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } = 2 , 4 , 6 , 8 , . . . 30 B = { b : b ∈ U and b is a multiple of 4 } = 4 , 8 , 12 , . . . 28 To find: A - B If P and Q are two sets, then their difference, i.e. P - Q is the set of those elements which belong to P but not to Q . Thus, A - B = { x : x ∈ A , x ∉ B | . A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. Therefore, A - B = 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 .

Given that, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } and B = { b : b ∈ U and b is a multiple of 4 } . Use Venn diagram to show B - A .

Given, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even} = 2 , 4 , 6 , 8 , . . . 30 , B = { b : b ∈ U and b is a multiple of 4 } = 4 , 8 , 12 , . . . 28 To find: B - A If P and Q are two sets, then their difference, i.e. P - Q is the set of those elements which belong to P but not to Q . Thus, B - A = x : x ∈ B , x ∉ A A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. Therefore, B - A = ϕ .

Given that, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } and B = { b : b ∈ U and b is a multiple of 4 } . Use Venn diagram to show n ( A ) .

Given, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } = 2 , 4 , 6 , 8 , . . . 30 B = { b : b ∈ U and b is a multiple of 4 } = 4 , 8 , 12 , . . . 28 To find: n ( A ) The number of distinct elements in a set is called the cardinal number of the set. The cardinal number of a set A is denoted by n A . A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. Therefore, n A = 15 .

Given that, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } and B = { b : b ∈ U and b is a multiple of 4 } . Use Venn diagram to show n ( B ) . Hence, prove that n ( A ∪ B ) = n ( A ) + n ( B ) - n ( A ∩ B ) .

Given, U = { x : x ∈ N , x ≤ 30 } , A = { a : a ∈ U and a is even } = 2 , 4 , 6 , 8 , . . . 30 B = { b : b ∈ U and b is a multiple of 4 } = 4 , 8 , 12 , . . . 28 We need to find: n ( B ) and to prove n ( A ∪ B ) = n ( A ) + n ( B ) - n ( A ∩ B ) The number of distinct elements in a set is called the cardinal number of the set. The cardinal number of a set A is denoted by n A . A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. From the Venn diagram, n A = 15 , n ( B ) = 7 , n ( A ∪ B ) = 15 and n A ∩ B = 7 LHS = n ( A ∪ B ) = 15 RHS = n ( A ) + n ( B ) - n ( A ∩ B ) = 15 + 7 - 7 ∴ LHS = RHS Hence, n ( A ∪ B ) = n ( A ) + n ( B ) - n ( A ∩ B ) .

E M B I B E

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise

S.N. Chhibber Solutions for Chapter: Operations on Sets, Exercise 5: Exercise

Author:S.N. Chhibber

S.N. Chhibber Mathematics Solutions for Exercise - S.N. Chhibber Solutions for Chapter: Operations on Sets, Exercise 5: Exercise

Attempt the practice questions on Chapter 1: Operations on Sets, Exercise 5: Exercise with hints and solutions to strengthen your understanding. Joy Of Mathematics 8 solutions are prepared by Experienced Embibe Experts.

Questions from S.N. Chhibber Solutions for Chapter: Operations on Sets, Exercise 5: Exercise with Hints & Solutions

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 4

In a class of $40$ students, $24$ like black colour and $18$ like white colour while $5$ like neither. Find the number of students who like both black and white colours. Draw a Venn diagram to represent it.

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 5

Meena gets a certain amount as pocket money. She spends one-fourth of it on stationery and one-third in the school canteen. If she saves $₹ 40$ , find the amount of pocket money she received and represent the data using Venn diagram.

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 6

Given that, $U = {x : x \in N, x \leq 30}, A = {a : a \in U and a is even}$ and $B = {b : b \in U and b is a multiple of 4} .$ Use Venn diagram to show $A \cap B$ .

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 6

Given that, $U = {x : x \in N, x \leq 30}, A = {a : a \in U and a is even}$ and $B = {b : b \in U and b is a multiple of 4} .$ Use Venn diagram to show $A - B$ .

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 6

Given that, $U = {x : x \in N, x \leq 30}, A = {a : a \in U and a is even}$ and $B = {b : b \in U and b is a multiple of 4} .$ Use Venn diagram to show $B - A$ .

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 6

Given that, $U = {x : x \in N, x \leq 30}, A = {a : a \in U and a is even}$ and $B = {b : b \in U and b is a multiple of 4} .$ Use Venn diagram to show $n (A)$ .

EASY

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 6

Given that, $U = {x : x \in N, x \leq 30}, A = {a : a \in U and a is even}$ and $B = {b : b \in U and b is a multiple of 4} .$ Use Venn diagram to show $n (B)$ .

Hence, prove that $n (A \cup B) = n (A) + n (B) - n (A \cap B)$ .

MEDIUM

8th CBSE

IMPORTANT

Joy Of Mathematics 8>Chapter 1 - Operations on Sets>Exercise>Q 7

In an examination, $90 %$ students passed in Hindi, $80 %$ students passed in maths, $6 %$ failed in both the subjects. Using Venn diagram, find the percentage of students passed in both the subjects.

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