Given the following sets, select the statement below that is NOT true.
A = {b, l, a, z, e, r}, B = {b, a, l, e}, C = {a, b, l, e}, D = {l, a, b}, E = {a, b, l}
E ⊂ C
E ⊆ B
D ⊆ B
B ⊂ C
C ⊆ A

Question

Given the following sets, select the statement below that is NOT true. 
A = {b, l, a, z, e, r}, B = {b, a, l, e}, C = {a, b, l, e}, D = {l, a, b}, E = {a, b, l}
       E ⊂ C
       E ⊆ B
       D ⊆ B
       B ⊂ C
       C ⊆ A

anonymous · Answer

Ah, now we're working with subsets

anonymous · Answer

yup... 
c is everything in element right?

anonymous · Answer

and the c with underline is everything thats NOT in element

anonymous · Answer

right?

anonymous · Answer

$$E \subset C$$
Is true only if every element in E is also in C BUT E does not equal C.

anonymous · Answer

$$E \subseteq C$$
Is true if every element in E is also in C.

anonymous · Answer

so if C has 5 elements and e has 2 elements it False right? even if they have some of the "same"

anonymous · Answer

No

anonymous · Answer

It's not about the number of elements

anonymous · Answer

oh boy! here we go again! lol

anonymous · Answer

its the same elements in each set right?

anonymous · Answer

New stuff put on the learning cap ;)

anonymous · Answer

okie dokie.. :)

anonymous · Answer

Ok lets start with the easier of the two.
$$E \subseteq B$$is true if ALL the items in E are also in B.

anonymous · Answer

Se what are the items in E? Is every one of those also in B?

anonymous · Answer

a,b,l

anonymous · Answer

Are all of those also in B?

anonymous · Answer

yes

anonymous · Answer

Then E is a subset of B. 
$E \subseteq B$ is True

anonymous · Answer

$E \subseteq B$ literally means 'E is a subset of B'

anonymous · Answer

Since we are looking for statements that are NOT true, this is not the right answer.

anonymous · Answer

ok

anonymous · Answer

lets look at the first option.
$E \subset C$
Is E a proper subset of C?

anonymous · Answer

the next one is E C underlined B =
E=a,b,l
B=b,a,l,e

anonymous · Answer

To be a proper subset 2 things have to be true. 

E must be a subset of C. 
E must not equal C.

anonymous · Answer

I was going back to the previous one we skipped cause it was tougher.

anonymous · Answer

The very first option on the list.

anonymous · Answer

$E \subset C$ means 'E is a proper subset of C'

anonymous · Answer

E=a,b,l 
C=a.b.l.e so yes is it is a subset

anonymous · Answer

So what do you think?

anonymous · Answer

Right but is it a proper one?

anonymous · Answer

For E to be a proper subset it has to be a subset, and it cannot be equal.

anonymous · Answer

yes cuz they e and c have same elements

anonymous · Answer

and its not equal cuz c has e in it also

anonymous · Answer

correct.

anonymous · Answer

so that would be False...

anonymous · Answer

Therefore since every element in E is also in C AND E does not equal C. E is a proper subset of C

anonymous · Answer

$E \subset C$ is True
E is a proper subset of C

anonymous · Answer

ok the C mean proper subset right?

anonymous · Answer

$\subset$ means proper subset.

anonymous · Answer

yea i dont know how to make that on here thats what i ment

anonymous · Answer

I figured =)

anonymous · Answer

and the line under the c means improper subset right?

anonymous · Answer

Yeah, improper subsets are usually just called 'subsets' with no distinction.

Ok so now you know about subsets and proper subsets. Lets have you take a stab at the next options.

anonymous · Answer

ok

anonymous · Answer

Since we haven't found any false ones yet.

anonymous · Answer

D ⊆ B
D = {l, a, b}
B = {b, a, l, e}
they both have {a,b,l} so it would be True

anonymous · Answer

It's not about what they both have. It's about is everything in D also in B.

anonymous · Answer

But yes, it's true.

anonymous · Answer

ok so it has every element in D and in B so it would be True

anonymous · Answer

Every element in D is also in B so it's true.

anonymous · Answer

I know you're probably thinking it right. But you're not saying it right, so I'm just ironing out the ambiguity.

anonymous · Answer

Sorry for being so pedantic. But I like to have things clear

anonymous · Answer

B ⊂ C
B = {b, a, l, e}, 
C = {a, b, l, e}
B and C has every element that in both so this is True

anonymous · Answer

Ah, but there is no line underneath

anonymous · Answer

is B a proper subset of C?

anonymous · Answer

It is a subset, I agree, but B = C doesn't it?

anonymous · Answer

No they have all the same elements

anonymous · Answer

Right. B = C therefore B is not a proper subset. It is an improper subset

anonymous · Answer

so it wouldnt be a proper subset. cuz one of them would need a differnt element to be a subset

anonymous · Answer

so it would be False

anonymous · Answer

C would need a different element.

anonymous · Answer

and to be an improper subset it should have the line under the c right?

anonymous · Answer

If B had a different element it would still be false because then not every element in B would also be in C and it wouldn't be a subset at all.

anonymous · Answer

right it would have to be $B \subseteq C$ to be true, or C would have to have an additional element,

anonymous · Answer

so this would be the answer cuz its False

anonymous · Answer

Correct. B is not a proper subset of C 
Therefore $B \subset C$ is False.

anonymous · Answer

ty hon.. i am getting the hang of this type of problems.. You explain it Very good :) and helped me out A LOT! Thank you :)

anonymous · Answer

No problem =)