Using Set Notation Effectively

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| By Thames
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Thames
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Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 20 | Updated: Nov 11, 2025
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1) Which of the following represents a set?

Explanation

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

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About This Quiz
Using Set Notation Effectively - Quiz

Sets have their own precise language. In this quiz, you’ll read, write, and interpret set notation with accuracy. Try this quiz to build fluency in mathematical communication.

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2) The symbol ∅ represents:

Explanation

∅ means a set with no elements.

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

Explanation

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

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

Explanation

Intersection = elements common to both sets.

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5) A ∩ ∅ = ∅ for any set A.

Explanation

Intersection with empty set gives nothing.

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6) For any set A, A ∪ ∅ = ?

Explanation

Union with empty set does not add new elements.

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

Explanation

Order does not matter in sets.

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

Explanation

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

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

Explanation

No common elements → disjoint.

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

Explanation

Both notations mean the same thing.

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

Explanation

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

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

Explanation

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

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

Explanation

Union = all elements from A and B without duplicates.

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

Explanation

Complement = all elements in U not in A.

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15) If A ⊆ B and B ⊆ A, then A = B.

Explanation

Mutual subsets imply sets are equal.

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

Explanation

Use union formula: n(A ∪ B) = n(A)+n(B)−n(A ∩ B) = 18+12−6 = 24.
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17) If rolling a die, the sample space S is:

Explanation

All possible outcomes of die roll are 1 through 6.

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18) Which region represents A′ ∩ B?

Explanation

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

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

Explanation

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

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20) For any set A, A ∩ U = ?

Explanation

Intersection with universal set leaves A unchanged.

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Which of the following represents a set?
The symbol ∅ represents:
If A = {1,2,3} and B = {1,2,3,4}, then A ⊆ B means:
If A = {1,2,3} and B = {2,3,4}, then A ∩ B = ?
A ∩ ∅ = ∅ for any set A.
For any set A, A ∪ ∅ = ?
If A = {1,2} and B = {2,1}, then A = B.
If A = {a,b,c,d}, then n(A) = ?
A = {1,3,5}, B = {2,4,6}. Then A ∩ B = ?
{ } and ∅ both represent the empty set.
If A = {2,4} and B = {2,4,6}, then A is:
Which describes the set {2,4,6,8}?
If A = {1,2} and B = {2,3}, then A ∪ B = ?
If U = {1,2,3,4,5} and A = {2,4}, then A′ = ?
If A ⊆ B and B ⊆ A, then A = B.
In a class of 30 students, 18 like math, 12 like physics, and 6 like...
If rolling a die, the sample space S is:
Which region represents A′ ∩ B?
If A = {x,y}, P(A) = ?
For any set A, A ∩ U = ?
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