Answer to Question #273562 in Discrete Mathematics for Albert

Question #273562

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}


1
Expert's answer
2021-12-02T12:21:59-0500

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

The statement 0 ∈ ø is False.


b.

Only one element of {0}\{0\} is , so {0}\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,}\{0,\varnothing\} are  and \varnothing, so {0,}\varnothing\in\{0,\varnothing\}

The statement ø ∈ {0, ø} is True.


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