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If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the number of subsets of A ∪ B?
If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the number of subsets of A ∪ B?
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Practice Questions
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Q1
If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the number of subsets of A ∪ B?
8
16
4
12
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A ∪ B = {1, 2, 3, 4}, which has 4 elements. The number of subsets is 2^4 = 16.
Questions & Step-by-step Solutions
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Q
Q: If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the number of subsets of A ∪ B?
Solution:
A ∪ B = {1, 2, 3, 4}, which has 4 elements. The number of subsets is 2^4 = 16.
Steps: 7
Show Steps
Step 1: Identify the sets A and B. A = {1, 2, 3} and B = {1, 2, 3, 4}.
Step 2: Find the union of sets A and B, which is A ∪ B. This means we combine all unique elements from both sets.
Step 3: List the elements in A ∪ B. The unique elements are {1, 2, 3, 4}.
Step 4: Count the number of elements in A ∪ B. There are 4 elements: 1, 2, 3, and 4.
Step 5: Use the formula for the number of subsets. The number of subsets of a set with n elements is 2^n.
Step 6: Since A ∪ B has 4 elements, calculate 2^4.
Step 7: Calculate 2^4, which equals 16. This is the total number of subsets of A ∪ B.
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