I know the following answers to this question but I'm unable to understand why some of them are so. Please explain to me the parts where I put a ??. Thank you.
which of the following statements are true A={1,{1},{2}}
1. 1 exists in A = True
2. {1} exists in A = True
3. {1} is a subset of A = True
4. {{1}} is a subset of A = True?? How??
5. {2} exists in A = True
6. {2} is a subset of A = False?? How??
7. {{2}} is a subset of A = True?? How??
8. {{2}} is a proper set of A = True. (I know this follows from 7)
What gets me the most is why 3 is true and 6 is false. I've tried looking in my book and online, but I can't find an example that tells me why. Thank you!
which of the following statements are true A={1,{1},{2}}
1. 1 exists in A = True
2. {1} exists in A = True
3. {1} is a subset of A = True
4. {{1}} is a subset of A = True?? How??
5. {2} exists in A = True
6. {2} is a subset of A = False?? How??
7. {{2}} is a subset of A = True?? How??
8. {{2}} is a proper set of A = True. (I know this follows from 7)
What gets me the most is why 3 is true and 6 is false. I've tried looking in my book and online, but I can't find an example that tells me why. Thank you!