Question

Given the following sets, select the statement below that is true.
A = {b, l, a, z, e, r}, B = {b, a, l, e}, C = {a, b, l, e}, D = {l, a, b}, E = {l,

D ⊆ E and C ⊂ A
B ⊆ C and B ⊆ E
E ⊆ B and B ⊆ C
B ⊂ E and D ⊆ A
D ⊆ E and E ⊂ A

Answer 1

Do you know what those symbols mean?

Answer 2

kinda

Answer 3

C with underline is improper subset. C means proper

Answer 4

what does it mean to be improper subset?

Answer 5

or proper for that matter.

Answer 6

i dont know that.. does say in the ebook:(

Answer 7

Ok. A subset (improper) is just a set that has some OR all of the same elements as the original.

That means that if \(Q \subseteq R\) Then every element in Q is also in R.

Answer 8

If instead we have \(P \subset R\) That means that every element in P is also in R BUT not every element in R is in P.

Answer 9

So P doesn't equal R. Q could equal R though.

Answer 10

So now that we know that. Lets look at your problem.

Answer 11

Oh.. Your E set got cut off.

Answer 12

Can you type it out for me?

Answer 13

A = {b, l, a, z, e, r}, B = {b, a, l, e}, C = {a, b, l, e}, D = {l, a, b}, E = {l, a}

Answer 14

D ⊆ E and C ⊂ A
B ⊆ C and B ⊆ E
E ⊆ B and B ⊆ C
B ⊂ E and D ⊆ A
D ⊆ E and E ⊂ A

Answer 15

so D and E have l,a the same

Answer 16

Ok. So the first choice:\[D\subseteq E \text{ and } C \subset A\]

Is each element of D also in E? Is each element in C also in A?

Answer 17

not all of them for D and E and yes all the same for C and A

Answer 18

Ok, so you have

\(\text{ False and True } \implies False\)

Therefore it is not the first option.

Answer 19

ok

Answer 20

B and C and B and E

Answer 21

So the second option:\[B \subseteq C \text{ and } B \subseteq E\]

Is each element in B also in C? And is each element in B also in E?

Answer 22

b and C have all the same elements

Answer 23

but b and E are same but different

Answer 24

so that would be True and False=False

Answer 25

Right.

Answer 26

Option 3?

Answer 27

E and B and B and C

Answer 28

Is E a subset of B?

Answer 29

no its not... same but differnent

Answer 30

Hold up

Answer 31

so it would be False and True =False

Answer 32

We don't care if they are the same.

Answer 33

That would be B = E

Answer 34

We want to know. Is every element in the subset also in the original set.

Answer 35

So in this case, Is E a subset of B. Is every element in E also in B?

Answer 36

even if B has other elements that arent the same?

Answer 37

Yes!

Answer 38

yes E is a subset of B

Answer 39

Right!

Answer 40

B is NOT a subset of E. But E IS a subset of B

Answer 41

and B and C have the same elements

Answer 42

Because l and a are both in B. And since B and C are the same, B is an improper subset of C also.

Answer 43

ok if it was switched around it would be false. cuz B dont have same elements as E

Answer 44

Right!

Answer 45

so my answer would be E and B and B and C

Answer 46

E subset B and B subset C yes.

Answer 47

ok now i starting to understand this a little bit more.

Answer 48

That's awesome. Keep practicing ;)

Answer 49

ty :)