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}}}
Question
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}}}
Solution
The power set Ƥ(A) is the set of all subsets of A. Given A = {1, 2, {1}}, the power set Ƥ(A) would include subsets like {}, {1}, {2}, {{1}}, {1, 2}, {1, {1}}, {2, {1}}, and {1, 2, {1}}.
Now, let's check the options:
a. {1} is a subset of A, so it is in Ƥ(A).
b. {1, 2, {1, 2}} is not a subset of A because {1, 2} is not an element of A.
c. {{{1}}} is not a subset of A because {{1}} is not an element of A.
d. {{{2}}} is not a subset of A because {{2}} is not an element of A.
So, the only subset of Ƥ(A) from the given options is a. {1}.
Similar Questions
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