If A = {x, y, z}, then the number of subsets in powerset of A is
8
Finding the Number of Subsets in a Power Set
The question asks us to determine the total count of subsets that can be formed from the power set of a given set A.
The set provided is A = {x, y, z}.
Understanding Power Sets
A power set of a set A, often denoted as P(A), is defined as the set containing all possible subsets of A, including the empty set and the set A itself.
Calculating the Number of Subsets
For any given finite set with n elements, the total number of subsets in its power set is given by the formula:
Number of subsets = $2^n$
In this specific problem, the set A = {x, y, z} contains 3 distinct elements. Therefore, the number of elements, n, is 3.
Using the formula, we can calculate the number of subsets in the power set of A:
Number of subsets = $2^3$
Calculating the value:
$2^3 = 2 \times 2 \times 2 = 8$
So, the power set of A will contain 8 subsets.
Conclusion
The number of subsets in the power set of A = {x, y, z} is 8.
Important Questions from Set Theory and types of Sets
- In a competitive examination, 80% candidates passed in section A, 77% in section B while 18% failed in both the sections. If 1425 students passed in both the sections, find the total number of candidates who appeared in the competitive examination.
- For any three non-empty sets \(A, B, C\), what is \((A \cup B) - \{(A - B) \cup (B - A) \cup (A \cap B)\}\) equal to ?
If A = {λ, {λ, μ}}, then the power set of A is
- Which of the following is not a convex set?
If A, B and C are subsets of a given set, then which one of the following relations is not correct?
