Question 480509
Determine whether A = B, A ⊆ B, B ⊆ A, A ⊂ B, B ⊂ A or if none of these answers applies.
A = {x | x is a sport that uses a ball}
B = {basketball, soccer, tennis}
<pre>

A = B   No A doesn't equal B because for instance, A contains baseball, golf,
etc. but B doesn't.

A &#8838; B  No, every element of A is not an element of B because for
instance, baseball is an element of A,  

B &#8838; A  Yes because, although B doesn't equal A by any means, every
element of B is also an element of A.

A &#8834; B  No, this is just like A &#8838; B except that A &#8838; B allows
but does not require, the possibility of A = B, whereas A &#8834; B doesn't
allow A = B.  But that's not any worry here.

B &#8834; A  Yes because every element of B is also an element of A.  The only
difference between &#8834; and &#8838; is that &#8834; does NOT allow the sets
on both sides of it to be exactly the same set, whereas &#8838; allows it but
does not require it.

         
So B &#8838; A and B &#8834; A are the only ones that hold.

Examples:

{a,r,t} = {t,a,r} is true because the order they're listed in doesn't matter
{a,r,t} &#8838; {t,a,r} is true because &#8838; allows (but doesn't require)
equality
{a,r,t} &#8834; {t,a,r} is false because &#8834; does not allow equality
{a,r,t} &#8834; {s,t,a,r} is true because every element of the left set is also
an element of the right set.  It doesn't allow equality but we surely don't
have that.
{a,r,t} &#8838; {s,t,a,r} is true because every element of the left set is also
an element of the right set.  It allows equality but doesn't require it.

Edwin</pre>