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If F = {x, y, z}, what is the size of the power set of F?

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Question: If F = {x, y, z}, what is the size of the power set of F?

Options:

  1. 3
  2. 6
  3. 8
  4. 12

Correct Answer: 8

Solution: 

The size of the power set is 2^n where n is the number of elements in the set. Here, n = 3, so the size is 2^3 = 8.

If F = {x, y, z}, what is the size of the power set of F?

Practice Questions

Q1
If F = {x, y, z}, what is the size of the power set of F?
  1. 3
  2. 6
  3. 8
  4. 12

Questions & Step-by-Step Solutions

If F = {x, y, z}, what is the size of the power set of F?
Correct Answer: 8
  • Step 1: Identify the set F. In this case, F = {x, y, z}.
  • Step 2: Count the number of elements in the set F. Here, there are 3 elements: x, y, and z.
  • Step 3: Use the formula for the size of the power set, 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 size of the power set of F is 8.
  • 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 size of the power set grows exponentially with the number of elements in the original set, specifically as 2^n.
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