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Class 12MathematicsSetsEasyLevel 9
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If A has 4 elements, how many elements does its power set P(A) have?

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Answer and explanation

Correct answer: 16

The power set P(A) is the set containing every subset of A, including the empty set and A itself. If a set has n elements, each element has two possibilities in a subset— it is either included or excluded—so the power set has 2^n elements. Here n = 4, giving |P(A)| = 2^4 = 16. Therefore, option C is correct.

Related tags

Power-SetCardinalitySubsetsSetsMathematicsClass 12 Mcq

Frequently asked questions

What is the correct answer to this question?

16

Why is this the correct answer?

The power set P(A) is the set containing every subset of A, including the empty set and A itself. If a set has n elements, each element has two possibilities in a subset— it is either included or excluded—so the power set has 2^n elements. Here n = 4, giving |P(A)| = 2^4 = 16. Therefore, option C is correct.

Which subject and chapter does this question cover?

This is a Class 12 Mathematics question. Chapter: Sets.

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  3. 3Which is the correct roster form of B = {x : x is a prime divisor of 84}?
  4. 4Which set best represents N = {2, 4, 8, 16, 32}?
  5. 5Which option is not an example of a well-defined set?
  6. 6What is the correct roster form of A₁ = {x : x ∈ ℕ, x² − 1 = 0}?
  7. 7If D₁ = {x : x ∈ ℤ, 2 < x² ≤ 16}, what is the roster form of D₁?
  8. 8The set E₁ = {x : x ∈ ℕ, x = 30/n, n ∈ ℕ} is equal to which set?
  9. 9Which option is the correct roster form of G₁ = {x : x ∈ ℤ, x³ = x}?
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