Set Language and Notations Questions

Basic Questions (Easy)

• Identify Set Members

1. Given A = {1,2,3,4} and B = {3,4,5,6} determine whether the following is true: a) 3∈A∩B b) 1∉B

Solution: a) Yes, 3∈A∩B3, as it is common to both A and B. b) True, as 1∉B

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• Union of Sets 

2. If X = {a,b,c} and Y = {b,c,d}, find X∪Y.

Solution: X∪Y = {a,b,c,d}

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Intermediate Questions

• Set Complement

3. Let the universal set U={1,2,3,4,5,6} and C = {2,4,6}. Find the complement of, C,C′.

Solution: C′ =U −C = {1,3,5}

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• Subset Verification

4. Given P={1,2} and Q={1,2,3,4}, verify whether P⊂Q and Q⊂P.

Solution:

• P⊂Qis true as all elements of P are in Q.
• Q⊂P is false as Q has additional elements not in P.

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Advanced Questions

• Multiple Operations

6, If M={2,4,6} and N={1,2,3,4} find: a) M∩N b) (M∪N), given U={1,2,3,4,5,6}

Solution:

1. a) M∩N={2,4}

b)M∪N={1,2,3,4,6}. (M∪N)′ = U − (M∪N) ={5}

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• Venn Diagram Problem

7. In a class of 40 students, 18 study Math, 24 study Science, and 10 study both. a) Represent this information on a Venn diagram. b) How many students study only Math? c) How many students study neither subject? Solution: a) Draw a Venn diagram with overlapping circles representing Math and Science. b) Only Math =18−10=8 c) Neither =40−(8+10+14)=8

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Challenging Questions

• General Problem-Solving

Let A= {x∈N∣x<10} and B= {x∈N∣5≤x≤15}. Find: a) A∩B b) A∪B

Solution: a) A∩B={5,6,7,8,9}

b) A∪B={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}|

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• Real-World Application

A survey of 100 people revealed:

• 60 like tea,
• 50 like coffee,
• 20 like both.

1. a) How many like only tea? b) How many like neither?

Solution: a) Only tea=60−20=40

1. b) Neither=100−(40+30+20)=10)

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