For the set E = {1, 2, 3, 4}, how many subsets contain the element 1?

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Question: For the set E = {1, 2, 3, 4}, how many subsets contain the element 1?

Options:

Correct Answer: 12

Solution:

If 1 is included, we can choose from the remaining elements {2, 3, 4}, which has 2^3 = 8 subsets.

For the set E = {1, 2, 3, 4}, how many subsets contain the element 1?

For the set E = {1, 2, 3, 4}, how many subsets contain the element 1?

Step 1: Identify the set E, which is {1, 2, 3, 4}.
Step 2: We want to find subsets that must include the element 1.
Step 3: Since 1 is included in every subset we are considering, we only need to focus on the remaining elements, which are {2, 3, 4}.
Step 4: Count the number of elements left after including 1. There are 3 elements: 2, 3, and 4.
Step 5: Each of these 3 elements can either be included in a subset or not. This gives us 2 choices (include or not) for each element.
Step 6: Calculate the total number of combinations for the remaining elements. Since there are 3 elements, the total number of subsets is 2^3.
Step 7: Calculate 2^3, which equals 8. This means there are 8 different subsets that include the element 1.

Subsets – Understanding how to form subsets from a given set and the concept of including or excluding specific elements.
Power Set – The total number of subsets of a set is calculated using the formula 2^n, where n is the number of elements in the set.