Determine whether each of the following is true or false. a. 0 ∈ ø b. ø ∈ {0} c. {ø} ⊆ {0} d. {ø} ⊆ {ø} e. ø ∈ {0, ø}
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a. ∅ (empty set, null set): the set with no members.
The statement 0 ∈ ø is False.
b.
Only one element of is , so
The statement ø ∈ {0} is False.
c. Every nonempty set S is guaranteed to have at least two subsets, the
empty set and the set S itself
The statement {ø} ⊆ {0} is True.
d.
Only one element of is , so every element of is an element of, that is .
The statement {ø} {ø} is True.
e.
Elements of are and , so
The statement ø ∈ {0, ø} is True.