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How many subsets does the set A = {a, b, c} have?

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Question: How many subsets does the set A = {a, b, c} have?

Options:

  1. 2
  2. 3
  3. 4
  4. 8

Correct Answer: 8

Solution: 

The number of subsets of a set with n elements is 2^n. Here, n = 3, so the number of subsets is 2^3 = 8.

How many subsets does the set A = {a, b, c} have?

Practice Questions

Q1
How many subsets does the set A = {a, b, c} have?
  1. 2
  2. 3
  3. 4
  4. 8

Questions & Step-by-Step Solutions

How many subsets does the set A = {a, b, c} have?
  • Step 1: Identify the set A. In this case, A = {a, b, c}.
  • Step 2: Count the number of elements in the set A. Here, there are 3 elements: a, b, and c.
  • Step 3: Use the formula for the number of subsets, which is 2^n, where n is the number of elements in the set.
  • Step 4: Substitute the value of n into the formula. Since n = 3, we calculate 2^3.
  • Step 5: Calculate 2^3, which equals 8.
  • Step 6: Conclude that the number of subsets of the set A = {a, b, c} is 8.
  • Subsets – A subset is a set formed from the elements of another set, including the empty set and the set itself.
  • Power Set – The power set of a set is the set of all possible subsets, including the empty set and the set itself.
  • Exponential Growth – The number of subsets grows exponentially with the number of elements in the set, specifically as 2^n.
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