True or False

Question

Let A={{x}},B={x,{x}},C={x,{x,{x,}}}

1) {} subset B
2) B proper subset C
3) A element B
4) x element A
5) B element C
6) A subset B

 

I really thought all were true however one said that numbers 2,3,4 are false. Why is that so? Please explain. Thank you!!

Answer 1

1) true, the null set is a subset of every set

2) false, x is in C but {x} is not in C although {x,{x}} is in C but {x} and{x,{x}} are two different elements

3) false, B contains x and {x} but not A; there is no A in set B

4) false, A contains {x} but does not contain x (x is missing the {})

5) false, C has no B in it (C contains x and {x,{x}} but no B)

6) true, {x} is in B and {x} is the only element in A