Let A = {{⊘}, 1, {1}}.Which one of the following alternatives regarding A is FALSE?a.{{1}} ⊂ Ab.{⊘} ⊂ Ac.|Ƥ (A)| = 8d.{⊘} ∈ AClear my choice
Question
Let A = {{⊘}, 1, {1}}. Which one of the following alternatives regarding A is FALSE?
a. {{1}} ⊂ A
b. {⊘} ⊂ A
c. |Ƥ (A)| = 8
d. {⊘} ∈ A
Solution
Let's analyze each alternative:
a. {{1}} ⊂ A: This is TRUE. The set {1} is an element of A, so the set containing {1} is a subset of A.
b. {⊘} ⊂ A: This is TRUE. The empty set is an element of A, so the set containing the empty set is a subset of A.
c. |Ƥ (A)| = 8: This is TRUE. The power set of A, denoted Ƥ(A), is the set of all subsets of A. Since A has three elements, its power set has 2^3 = 8 elements.
d. {⊘} ∈ A: This is FALSE. While the empty set is an element of A, the set containing the empty set is not an element of A, but a subset.
So, the FALSE statement is d. {⊘} ∈ A.
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