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If D = {a, b}, how many subsets does D have?

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Question: If D = {a, b}, how many subsets does D have?

Options:

  1. 2
  2. 3
  3. 4
  4. 5

Correct Answer: 4

Solution: 

The number of subsets of a set with n elements is 2^n. Here, n = 2, so 2^2 = 4.

If D = {a, b}, how many subsets does D have?

Practice Questions

Q1
If D = {a, b}, how many subsets does D have?
  1. 2
  2. 3
  3. 4
  4. 5

Questions & Step-by-Step Solutions

If D = {a, b}, how many subsets does D have?
Correct Answer: 4
  • Step 1: Identify the set D. In this case, D = {a, b}.
  • Step 2: Count the number of elements in the set D. Here, there are 2 elements: a and b.
  • 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 = 2, we calculate 2^2.
  • Step 5: Calculate 2^2, which equals 4.
  • Step 6: Conclude that the number of subsets of the set D is 4.
  • 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 of Subsets – The number of subsets of a set with n elements is calculated using the formula 2^n.
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