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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}}}

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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}}}

This problem has been solved

Similar Questions

Consider the sets:U = {1, 2, {1}, {2}, {1, 2}}     A = {1, 2, {1}}      B = {{1}, {1, 2}}     C = {2, {1}, {2}}A – B is the set:a.{1, 2}b.{1, {1, 2}}c.{ }d.{{1, 2}}

U = {1, 2, {1}, {2}, {1, 2}}      A = {1, 2, {1}}       B = {{1}, {1, 2}}       C = {2, {1}, {2}}.Which one of the following sets represents both Ƥ (A) ⋂ Ƥ (B) and Ƥ (A ⋂ B)?a.{{1}}b.{⊘, {{1}}}c.{⊘, {1}}d.Not one of the above alternatives since Ƥ (A) ⋂ Ƥ (B) ≠ Ƥ (A ⋂ B)

U = {1, 2, {1}, {2}, {1, 2}}       A = {1, 2, {1}}      B = {{1}, {1, 2}}       C = {2, {1}, {2}}.Which one of the following is a subset of Ƥ (A)?(Remember, subsets of some set G can be formed by keeping the outside brackets of G and then throwing away none, one or more elements of G. Refer to study guide, p 40.)a.{1}b.{1, 2, {1, 2}}c.{{{1}}}d.{{{2}}}

U = {1, 2, {1}, {2}, {1, 2}}      A = {1, 2, {1}}       B = {{1}, {1, 2}}     C = {2, {1}, {2}}.Which one of the following statements is valid if x ∉ B U C? (Hint: Determine U – (B U C).)a.x ∈ {1}.b.x ∈ ⊘.c.x ∈ {1, 2}.d.x ∈ B and x ∈ C.

If 𝐴×𝐵 = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set B.

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