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## Homework Statement

Show that the intersection of Ai (for all i in I = {1, 2, 3, ... n } = A1. Ai is a subset of Aj whenever i <= j.

## Homework Equations

## The Attempt at a Solution

Show:

***I'm having trouble showing part 1***1. that the intersection of Ai is a subset of A1, and

2. A1 is a subset of the intersection of Ai.

This is my attempt: 1. Let x be an element of the intersection of Ai. Then x is in Ai for all i in I. Since A1 is contained in all Ai, then x is contained in A1.

2. Let x be an element of A1, then as A1 is a subset of Aj, for all j >= 1, x is an element of Aj. Thus, x is an element of the intersection of Ai.