Solution to Determine whether each of the following is true or false. a. 0 ∈ ø b. … - Sikademy
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Archangel Macsika

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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Here's the Solution to this Question

a. ∅ (empty set, null set): the set with no members.

The statement 0 ∈ ø is False.


b.

Only one element of \{0\} is , so \varnothing\notin\{0\}

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 \{\varnothing\} is \{\varnothing\}, so every element of \{\varnothing\} is an element of, that is \{\varnothing\}⊆\{\varnothing\}.

The statement {ø} {ø} is True.


e.

Elements of \{0,\varnothing\} are  and \varnothing, so \varnothing\in\{0,\varnothing\}

The statement ø ∈ {0, ø} is True.

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