Write T if the statement is true; write F otherwise

Question

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

 

i. {} subset B

ii. B proper subset C

iii. A element B

iv. x element A

v. B element C

vi. A subset B

 

I just want to compare my answers. Thanks! I'm glad that you're able to answer it.

Answer 1

Here's what I got:

 

 

i.  T.  {} is a subset of ALL sets.

 

ii.  F.  C has two elements -- x and {x,{x}}.  B has two elements -- x and {x}.  In order for B to be a subset of C, all the elements of B would have to be elements of C as well.  But {x} is an element of B but NOT an element of C. 

 

iii.  F.  B has two elements -- x and {x}.  A is {{x}}, and that is NOT one of the elements of B.

 

iv. F.  A has one element -- {x}.  That is not the same a x.  So x is not an element of A. 

 

v. T.  C has two elements -- x and {x,{x}}.  B is {x,{x}}, which is one of the elements of C.

 

vi.  T.  A has one element -- {x}.  B has two elements -- x and {x}.  A's one element is also an element of B, so A is a subset of B.