Consider the sets:U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}Ƥ (A) is the set:a.{⊘, {1}, {2}, {1, 2}, {1, 2, {1}}}b.{⊘, {1}, {2}, {{1}}, {1, 2}, {1, {1}}, {2, {1}}, {1, 2, {1}}}c.{⊘, {1}, {2}, {{1, 2}}, {1, {1}}, {2, {1}}, {1, 2, {1, 2}}}d.{⊘, {1}, {2}, {{1}}, {1, {1}}, {2, {1}}, {1, 2, {1}}}
Question
Consider the sets:U = {1, 2, {1}, {2}, {1, 2}} A = {1, 2, {1}} B = {{1}, {1, 2}} C = {2, {1}, {2}}Ƥ (A) is the set:a.{⊘, {1}, {2}, {1, 2}, {1, 2, {1}}}b.{⊘, {1}, {2}, {{1}}, {1, 2}, {1, {1}}, {2, {1}}, {1, 2, {1}}}c.{⊘, {1}, {2}, {{1, 2}}, {1, {1}}, {2, {1}}, {1, 2, {1, 2}}}d.{⊘, {1}, {2}, {{1}}, {1, {1}}, {2, {1}}, {1, 2, {1}}}
Solution
The power set of a set A, denoted by P(A), is the set of all possible subsets of A.
Given A = {1, 2, {1}}, the power set P(A) would include the empty set (denoted as ⊘), and all possible combinations of elements in A.
So, P(A) would be:
- The empty set: {⊘}
- The sets with one element: {1}, {2}, {{1}}
- The sets with two elements: {1, 2}, {1, {1}}, {2, {1}}
- The set with three elements: {1, 2, {1}}
Therefore, the correct answer is:
b. {⊘, {1}, {2}, {{1}}, {1, 2}, {1, {1}}, {2, {1}}, {1, 2, {1}}}
Similar Questions
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