Suppose that A, B, and C are sets such that A ? B and B ?

Chapter 1, Problem 17E

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QUESTION:

Problem 17E

Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.

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QUESTION:

Problem 17E

Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.

ANSWER:

Solution:

Step 1:

     In this problem we need to show that , suppose  A , B and C are sets such that  , and   then

   

 NOTE: 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.That is  and

                                               

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