Question: If E = {1, 2}, how many elements are in the power set of E?
Options:
2
4
3
1
Correct Answer: 4
Solution:
The power set of a set with n elements has 2^n elements. Here, n = 2, so 2^2 = 4.
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?
2
4
3
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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