If G = {1, 2, 3}, how many subsets contain the element '1'?
Practice Questions
1 question
Q1
If G = {1, 2, 3}, how many subsets contain the element '1'?
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The subsets containing '1' can be formed by including '1' and choosing from the remaining elements {2, 3}. There are 2^2 = 4 subsets, but we need to exclude the empty subset, so there are 4 - 1 = 3 subsets containing '1'.
Questions & Step-by-step Solutions
1 item
Q
Q: If G = {1, 2, 3}, how many subsets contain the element '1'?
Solution: The subsets containing '1' can be formed by including '1' and choosing from the remaining elements {2, 3}. There are 2^2 = 4 subsets, but we need to exclude the empty subset, so there are 4 - 1 = 3 subsets containing '1'.
Steps: 9
Step 1: Identify the set G, which is {1, 2, 3}.
Step 2: We want to find subsets that must include the element '1'.
Step 3: If we include '1' in our subsets, we can choose to include or not include the other elements {2, 3}.
Step 4: The remaining elements {2, 3} can either be included or excluded in each subset. This gives us 2 choices for '2' and 2 choices for '3'.
Step 5: Calculate the total combinations of including or excluding '2' and '3'. Since there are 2 elements, we have 2^2 = 4 combinations.
Step 6: The 4 combinations are: {1}, {1, 2}, {1, 3}, and {1, 2, 3}.
Step 7: All these subsets contain the element '1'.
Step 8: We do not need to exclude any subsets because all of them contain '1'.
Step 9: Therefore, the total number of subsets containing '1' is 4.
