Question: If F = {a, b, c}, how many subsets contain exactly 2 elements?
Options:
3
4
2
1
Correct Answer: 3
Solution:
The subsets containing exactly 2 elements are {a, b}, {a, c}, and {b, c}. So, there are 3 such subsets.
If F = {a, b, c}, how many subsets contain exactly 2 elements?
Practice Questions
Q1
If F = {a, b, c}, how many subsets contain exactly 2 elements?
3
4
2
1
Questions & Step-by-Step Solutions
If F = {a, b, c}, how many subsets contain exactly 2 elements?
Step 1: Identify the set F, which contains the elements {a, b, c}.
Step 2: Understand that a subset is a combination of elements from the set F.
Step 3: We need to find subsets that contain exactly 2 elements.
Step 4: List all possible combinations of 2 elements from the set F.
Step 5: The combinations are: {a, b}, {a, c}, and {b, c}.
Step 6: Count the number of combinations found in Step 5.
Step 7: The total number of subsets containing exactly 2 elements is 3.
Combinatorics – The question tests the understanding of how to calculate the number of combinations of a set, specifically choosing 2 elements from a set of 3.
Subsets – It assesses the ability to identify and list subsets of a given set.
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