Quick true and false questions: Subsets and Elements?

(a) {{∅}} ∈ {∅, {∅}}? TRUE


{{∅}} ⊆ {∅, {∅}}? TRUE





(b) {{∅}} ∈ {∅, {{∅}}}? TRUE


{{∅}} ⊆ {∅, {{∅}}}? TRUE





(c) {{∅}} ∈ {∅, {∅, {∅}}}? FALSE


{{∅}} ⊆ {∅, {∅, {∅}}}? FALSE








Just wanted to check my answers with anyone.


Thanks for any help or corrections.Quick true and false questions: Subsets and Elements?
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.Quick true and false questions: Subsets and Elements?
Count the brackets!





(a) {{∅}} ∈ {∅, {∅}}? False


{{∅}} ⊆ {∅, {∅}}? TRUE





(b) {{∅}} ∈ {∅, {{∅}}}? TRUE


{{∅}} ⊆ {∅, {{∅}}}? FALSE





(c) {{∅}} ∈ {∅, {∅, {∅}}}? FALSE


{{∅}} ⊆ {∅, {∅, {∅}}}? TRUE