Question

Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that
A ⊂ C?. If not, give an example. Please reply fast...

Answer 1

\[A \in (B \subset C) \implies (A \in B) \subset C \implies A \subset C\]
@leena1996

Answer 2

exactly but the answer key says its not so......it says A is not a subset of C......this is a question from NCERT Textbook Maths class 11........please clarify the doubt....

Answer 3

Let's give each set elements.\[A=\left\{ 1 \right\}\]\[B=\left\{ 1,2,3,4,5,6 \right\}\]\[C=\left\{ 1,2,3,4,5,6,7,8,9 \right\}\] Through this interpretation, it is clear that:\[A \in (B \subset C) \implies A \subset (B \subset C) \implies A \subset C\] In other words, your textbook is wrong.
@leena1996

Answer 4

thanks wanted to know that i am right......but are u sure that the text book is wrong cuz at this site it says: http://www.meritnation.com/discuss/question/2068778 please see this and confirm if the text was right....

Answer 5

I honestly don't know where they're getting that from, but I'm pretty sure that they're wrong. If you replace {x} with A for B and C in the solutions they try to provide, it's blatantly obvious that A is a subset of B and C. Unless I'm missing something really important here, I'm pretty sure they're wrong.

Answer 6

@leena1996

Answer 7

okk...thanks a lot!! i also got the same answer as you did.... Can you explain me this statement : "an element of a set can never be a subset of itself."

Answer 8

I think you are actually wrong

Answer 9

That's great to see someone call us wrong, can you tell me why?

Answer 10

See A is an element of C but not a subset of C

Answer 11

There is a diff

Answer 12

i did not get you @swissgirl

Answer 13

if it is an element that means it is present in C hence it needs to be a subset right.???

Answer 14

guys please tell me how to solve this.... i need the answer asap...

Answer 15

I am busy right now but when I am free I will explain

Answer 16

"In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment."

"Definitions

If A and B are sets and every element of A is also an element of B, then:
A is a subset of (or is included in) B..."

Courtesy of Wikipedia.

If: A = {a} B = {{a}, b} C = {{a}, b, c}

From this, we can say the following:\[A \subset C\]

Answer 17

alright thanks @genius12 , lets see what others have to say about this later....for now i accept this as the correct answer....

Answer 18

http://math.stackexchange.com/questions/131309/set-theory-difference-between-belong-contained-and-includes-subset
check this link out

Answer 19

@swissgirl I dont understand it still plz elaborate and explain......

Answer 20

@leena1996 Look what I found:

http://www.enotes.com/homework-help/let-b-c-three-sets-an-element-b-b-subset-c-true-327497

Answer 21

@genius12 i am not there on enotes so i cant view the whole answer...... hey i am gonna go offline for a while and return back after an hour or so.....until then if you guys find any answer please tell me

Answer 22

But look at what it says, the guy who answered the question is an expert on the topic. And according to him, my answer and your answer is correct. Everyone else who has a different answer is wrong. A is a subset of C and that is clearly implied by the information given. That's it, solved. You don't need to think about this more.

@leena1996

Answer 23

alright cud u see the answer.......are u there on enotes??

Answer 24

don't you see, read the first sentence, that's the answer. the rest of the words not shown is just an explanation for why that's the answer.

Answer 25

alright got it,.....thanks @genius12