If G = {1, 2, 3}, how many subsets contain the element '1'?

If G = {1, 2, 3}, how many subsets contain the element '1'?

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.

Subsets – Understanding how to form subsets from a set and the role of specific elements in those subsets.
Counting Principles – Applying the principles of counting to determine the number of subsets that include a specific element.