Let A = {{⊘}, 1, {1}}.Which one of the following alternatives regarding A is FALSE?a.{{1}} ⊂ Ab.{⊘} ⊂ Ac.|Ƥ (A)| = 8d.{⊘} ∈ AClear my choice

U = {a, b, c, d, e}    A = {d, e}    B = {a, b, c}.Which one of the following statements regarding the sets U, A and B is TRUE?a.| Ƥ (U) | = | Ƥ (A) | + | Ƥ (B)|b.⊘ ⊂ Ƥ (A) and ⊘ ⊂ Ƥ (B)c.U – A = A – Ud.A + B = U

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}}}

Which of the following is not equal to set A?

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)

Determine the truth values of the following propositions. Explain.a) ∅ ∈ {1}b) {1} ∈ {1}c) {1} ⊂ {1}d) {1} ∈ {1, {1}}e) {1} ⊆ {1, {1}}f) {{1}} ∈ 𝒫({1, {1}})