Question: If K = {a, b, c}, what is the number of subsets of K that do not contain the element \'a\'?
Options:
2
4
3
1
Correct Answer: 3
Solution:
If \'a\' is excluded, we can form subsets from {b, c}, which has 2^2 = 4 subsets.
If K = {a, b, c}, what is the number of subsets of K that do not contain the ele
Practice Questions
Q1
If K = {a, b, c}, what is the number of subsets of K that do not contain the element 'a'?
2
4
3
1
Questions & Step-by-Step Solutions
If K = {a, b, c}, what is the number of subsets of K that do not contain the element 'a'?
Step 1: Identify the set K, which is {a, b, c}.
Step 2: Determine that we want subsets that do not include the element 'a'.
Step 3: Remove 'a' from the set K, leaving us with the set {b, c}.
Step 4: Calculate the number of subsets of the remaining set {b, c}.
Step 5: Use the formula for the number of subsets, which is 2 raised to the power of the number of elements in the set.
Step 6: The set {b, c} has 2 elements, so we calculate 2^2.
Step 7: Calculate 2^2, which equals 4.
Step 8: Conclude that there are 4 subsets of K that do not contain the element 'a'.
Subsets – Understanding how to calculate the number of subsets of a set, particularly when certain elements are excluded.
Power Set – The concept of a power set, which is the set of all subsets of a given set, and how to determine the number of subsets based on the number of elements.
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