A = ∅, B = {∅, ∅}, C = {{∅}}, D = {{∅}, ∅}, E = {∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}}}.
(a) Determine the cardinality of each of the sets above.
(b) Write out the power set of each of the sets above.
(c) What are A ∩ B, A ∪ B, C ∩ D, C ∪ D, E − D, D − E, (D ∩ C) ∪ B
(d) What are A × B, B × A, D × E E × D
(e) Which of the following are true? A ∈ A, A ⊆ A, A ( A, A ∈ B, A ⊆ B, A ( B, A ∈ C, A ⊆ C, A ( C, A ∈ D, A ⊆ D, A ( D, A ∈ E, A ⊆ E, A ( E, B ∈ A, B ⊆ A, B ( A, B ∈ B, B ⊆ B, B ( B, B ∈ C, B ⊆ C, B ( C, B ∈ D, B ⊆ D, B ( D, B ∈ E, B ⊆ E, B ( E, C ∈ A, C ⊆ A, C ( A, C ∈ B, C ⊆ B, C ( B, C ∈ C, C ⊆ C, C ( C, C ∈ D, C ⊆ D, C ( D, C ∈ E, C ⊆ E, C ( E, D ∈ A, D ⊆ A, D ( A, D ∈ B, D ⊆ B, D ( B, D ∈ C, D ⊆ C, D ( C, D ∈ D, D ⊆ D, D ( D, D ∈ E, D ⊆ E, D ( E, E ∈ A, E ⊆ A, E ( A, E ∈ B, E ⊆ B, E ( B, E ∈ C, E ⊆ C, E ( C, E ∈ D, E ⊆ D, E ( D, E ∈ E, E ⊆ E, E ( E, A = B, A = C, A = D, B = D, C = D.
A = ∅, B = {∅, ∅}, C = {{∅}}, D = {{∅}, ∅}, E = {∅, {∅}, {∅, {∅}}, {∅, {∅}, {∅, {∅}}}}. (a) Determine the cardinality of each of the sets above. (b) Write out the power set of each of the sets above. (c) What are A ∩ B, A ∪ B, C ∩ D, C ∪ D, E − D, D − E, (D ∩ C) ∪ B (d) What are A × B, B ×...
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