Answer to Question #170952 in Discrete Mathematics for Aaron

Question #170952

Let A, B and C are sets. Prove that ≤ is transitive.                                                       (5 marks)



1
Expert's answer
2021-03-15T09:39:37-0400

To show that \subset is transitive we are to prove the following statement:

If ABA\subset B and BCB\subset C then ACA\subset C.

Let x be an element of A.

Since xAx\in A and ABA\subset B then xBx\in B.

Since xBx\in B and BCB\subset C then xCx\in C.

Therefore x xAxC\forall x\ x\in A\to x\in C and this means ACA\subset C .

The statement is proved.


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