If G = {x, y, z}, how many subsets contain exactly 2 elements?

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Question: If G = {x, y, z}, how many subsets contain exactly 2 elements?

Options:

Correct Answer: 3

Solution:

The subsets containing exactly 2 elements are {x, y}, {x, z}, and {y, z}. So, there are 3 such subsets.

If G = {x, y, z}, how many subsets contain exactly 2 elements?

If G = {x, y, z}, how many subsets contain exactly 2 elements?

Step 1: Identify the set G, which contains the elements {x, y, z}.
Step 2: Understand that a subset is a smaller group made from the elements of G.
Step 3: We need to find subsets that contain exactly 2 elements.
Step 4: List all possible combinations of 2 elements from the set G.
Step 5: The combinations are: {x, y}, {x, z}, and {y, z}.
Step 6: Count the number of combinations found in Step 5.
Step 7: The total number of subsets with exactly 2 elements is 3.

Combinatorics – The question tests the understanding of how to calculate combinations, specifically choosing 2 elements from a set of 3.