Quick true and false questions: Subsets and Elements?

Question

(a) {{∅}} ∈ {∅, {∅}}? TRUE
{{∅}} ⊆ {∅, {∅}}? TRUE

(b) {{∅}} ∈ {∅, {{∅}}}? TRUE
{{∅}} ⊆ {∅, {{∅}}}? TRUE

(c) {{∅}} ∈ {∅, {∅, {∅}}}? FALSE
{{∅}} ⊆ {∅, {∅, {∅}}}? FALSE


Just wanted to check my answers with anyone.
Thanks for any help or corrections.

Answer 1

The second part of c is false.
The set on the right hand side contains 2 elements, ∅ and {∅, {∅}}. The set on the left hand side contains only {∅} which is not one of the elements of the right hand side. Therefore it isn't a subset.

Everything else that pbb1001 answered looks right.

An important thing to understand in all of these is the difference between ∈ and ⊆. The ∈ symbol means "is an element of". Which means that whatever is to the left of the symbol must be an element that is in the set to the right. The ⊆ symbol means "is a subset of". So whatever is to the left is a set. And the elements inside this set are also inside the set to the right.

Answer 2

I'm now not a very devout individual, however I'm now not an atheist both. I got here to phrases with my possess individual problems related to God and being homosexual decades in the past. I'm secure believing that if a individual has a well middle, is sort to others, does well matters for persons and by some means or yet another makes a optimistic contribution to society (or a minimum of attempts to), then on the finish of that individual's existence God will smile down on them and take delivery of them with open hands.

Answer 3

Count the brackets!

(a) {{∅}} ∈ {∅, {∅}}? False
{{∅}} ⊆ {∅, {∅}}? TRUE

(b) {{∅}} ∈ {∅, {{∅}}}? TRUE
{{∅}} ⊆ {∅, {{∅}}}? FALSE

(c) {{∅}} ∈ {∅, {∅, {∅}}}? FALSE
{{∅}} ⊆ {∅, {∅, {∅}}}? TRUE