# Let A, B, and C be three sets. If A is an element of B and B is subset of C, is it true that A is subset C? If not explain with two examples.

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### 1 Answer

**If A is an element of B and B is a subset of C, then A is a subset of C.**

B is a subset of C implies that every element of B is contained in C. Since A is an element of B, it must be an element of C.

** If you meant to start with 3 sets A,B,C and `a in A,a in B,B sub C` then the answer is false. Here we just know that a(an element) lies in C, as opposed to the whole set A being contained in C.

Let A be the even numbers, B be the multiples of 3, and C be the multiples of 6. a=6 is clearly in A,B, and C, but A is not a subset of either B or C.

Let A be the set of rational numbers, B the set of natural numbers and C the set of integers. Then a=3 is clearly in B and C, but A is not a subset of B or C.

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