Thread: Sets & Subsets

I am having trouble with this thing. It says,

Let A={ø, {ø}, {{ø}}}.

(a) Determine which of the following are elements of A: ø, {ø}, {ø,{ø}}.

(b) Determine |A|

(c) Determine which of the following are subsets of A: ø, {ø}, {ø,{ø}}.

For d-i, determine the indicated sets.
(d) ø∩A

(e) {ø}∩A

(f) {ø,{ø}}∩A

(g) ø∪A

(h) {ø}∪A

(i) {ø,{ø}}∪A


For A, I got ø, {ø}
B, 3
C, ø,{ø}
D, ø
E, {ø}
F, nothing

Now, I'm just not sure what I'm doing. It's all these stupid empty sets.

Originally Posted by dude15129

I am having trouble with this thing. It says,

Let A={ø, {ø}, {{ø}}}.

(a) Determine which of the following are elements of A: ø, {ø}, {ø,{ø}}.

(b) Determine |A|

(c) Determine which of the following are subsets of A: ø, {ø}, {ø,{ø}}.

For d-i, determine the indicated sets.
(d) ø∩A

(e) {ø}∩A

(f) {ø,{ø}}∩A

(g) ø∪A

(h) {ø}∪A

(i) {ø,{ø}}∪A


For A, I got ø, {ø}
B, 3
C, ø,{ø}
D, ø
E, {ø}
F, nothing

Now, I'm just not sure what I'm doing. It's all these stupid empty sets.

My attempted solutions are as follows:

For C, ø, {ø}, {{ø}}, {ø,{ø}} are all subsets of A.
For F, {ø,{ø}}
For G,H,I, the answer is A.

I have the same answer with you except the above.