# I am unable to understand the following question and its solution related to "sets".Please explain it for me.Question-Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true thatA ⊂ C?....

I am unable to understand the following question and its solution related to "sets".Please explain it for me.

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.

Solution-No.Let A={1},B={{1}, 2} and C = {{1}, 2, 3}. Here A ∈ B as A = {1}

and B ⊂ C. But A ⊄ C as 1 ∈ A and 1 ∉ C.

Note that an element of a set can never be a subset of itself.

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### 1 Answer

The given proposition that is A o B and B 0C is true , then A o C need not be true.

We opt for to be & ( meaning intersection in set language).

Example : A = {1, 2 , 3} , B = { 1,2,3,4,5}, C = {4,5, 67}.

Then A & B = {2,3} is true. Or A intersects B is true.

B & C = {4,5} is true . Or B intersets C is true.

But the A intersects B and Bintersects C are both true inthe example. But this does mean or imply A intersets C. So A& C is false.

Given solution in the posted problem:

A = {1}

B= {{1}, 2} is not correct. {1} is a set and can not be an element .

C = { {1}, 2, 3}. The defintion of this set is not correct. {1} is a set . 2 and 3 are elements.

A set of sets is a class. So B and C are neither sets nor classes.