Answer to Question #273562 in Discrete Mathematics for Albert

Question

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}

Answer 1

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.