Using Set Notation Effectively

1) Which of the following represents a set?

{2, 4, 6, 8}

3 + 4

The tallest student in class

Running fast

A set is a well-defined collection of distinct elements.

Explanation

A set is a well-defined collection of distinct elements.

2) The symbol ∅ represents:

Universal set

Null set (empty set)

Complement of a set

Intersection of sets

∅ means a set with no elements.

Explanation

∅ means a set with no elements.

3) { } and ∅ both represent the empty set.

True

False

Both notations mean the same thing.

Explanation

Both notations mean the same thing.

4) If A = {1,2,3} and B = {1,2,3,4}, then A ⊆ B means:

A is equal to B

A is a subset of B

A is not related to B

A contains B

All elements of A are inside B → A ⊆ B.

Explanation

All elements of A are inside B → A ⊆ B.

5) If A = {2,4} and B = {2,4,6}, then A is:

Equal to B

A subset but not proper

A proper subset

Not a subset

A ⊂ B because A is inside B but not equal.

Explanation

A ⊂ B because A is inside B but not equal.

6) If A = {1,2} and B = {2,3}, then A ∪ B = ?

{1,2}

{2,3}

{1,2,3}

{1,3}

Union = all elements from A and B without duplicates.

Explanation

Union = all elements from A and B without duplicates.

7) If A = {1,2,3} and B = {2,3,4}, then A ∩ B = ?

{1,2,3,4}

{2,3}

{1,4}

{1,2}

Intersection = elements common to both sets.

Explanation

Intersection = elements common to both sets.

8) If U = {1,2,3,4,5} and A = {2,4}, then A′ = ?

{2,4}

{1,3,5}

{1,2,3,4,5}

{5}

Complement = all elements in U not in A.

Explanation

Complement = all elements in U not in A.

9) A ∩ ∅ = ∅ for any set A.

True

False

Intersection with empty set gives nothing.

Explanation

Intersection with empty set gives nothing.

10) If rolling a die, the sample space S is:

{1,2,3,4}

{1,2,3,4,5,6}

{even numbers}

{prime numbers}

All possible outcomes of die roll are 1 through 6.

Explanation

All possible outcomes of die roll are 1 through 6.

11) For any set A, A ∪ ∅ = ?

∅

A

Universal set

Undefined

Union with empty set does not add new elements.

Explanation

Union with empty set does not add new elements.

12) For any set A, A ∩ U = ?

∅

A

Universal set

A′

Intersection with universal set leaves A unchanged.

Explanation

Intersection with universal set leaves A unchanged.

13) Which describes the set {2,4,6,8}?

{x | x is odd}

{x | x is an even number ≤ 8}

{x | x is prime}

{x | x < 0}

The set is even numbers less than or equal to 8.

Explanation

The set is even numbers less than or equal to 8.

14) If A = {1,2} and B = {2,1}, then A = B.

True

False

Order does not matter in sets.

Explanation

Order does not matter in sets.

15) If A = {a,b,c,d}, then n(A) = ?

2

3

4

5

Cardinality n(A) = number of elements = 4.

Explanation

Cardinality n(A) = number of elements = 4.

16) A = {1,3,5}, B = {2,4,6}. Then A ∩ B = ?

∅

{1,2,3,4,5,6}

{1,2}

{5,6}

No common elements → disjoint.

Explanation

No common elements → disjoint.

17) If A = {x,y}, P(A) = ?

{x,y}

{∅,{x,y}}

{∅,{x},{y},{x,y}}

{x,{y}}

Power set = all subsets, including ∅ and A itself.

Explanation

Power set = all subsets, including ∅ and A itself.

18) Which region represents A′ ∩ B?

Only in A

Only in B but not in A

In both A and B

Outside A and B

‘Not A AND B’ means elements only in B but not A.

Explanation

‘Not A AND B’ means elements only in B but not A.

19) If A ⊆ B and B ⊆ A, then A = B.

True

False

Mutual subsets imply sets are equal.

Explanation

Mutual subsets imply sets are equal.

20) In a class of 30 students, 18 like math, 12 like physics, and 6 like both. How many like math OR physics?

24

30

20

18

Use union formula: n(A ∪ B) = n(A)+n(B)−n(A ∩ B) = 18+12−6 = 24.

Explanation

Use union formula: n(A ∪ B) = n(A)+n(B)−n(A ∩ B) = 18+12−6 = 24.