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If E = {1, 2}, how many elements are in the power set of E?

Practice Questions

Q1
If E = {1, 2}, how many elements are in the power set of E?
  1. 2
  2. 4
  3. 3
  4. 1

Questions & Step-by-Step Solutions

If E = {1, 2}, how many elements are in the power set of E?
  • Step 1: Identify the set E. In this case, E = {1, 2}.
  • Step 2: Count the number of elements in the set E. Here, there are 2 elements (1 and 2).
  • Step 3: Use the formula for the power set, which is 2^n, where n is the number of elements in the set.
  • Step 4: Substitute n with the number of elements in E. So, we calculate 2^2.
  • Step 5: Calculate 2^2, which equals 4.
  • Step 6: Conclude that the power set of E has 4 elements.
  • 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 elements in the power set grows exponentially with the number of elements in the original set, specifically as 2^n.
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