Answered: How do you show the image of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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How do you show the image of the intersecction of S and T is a subset of the intersection of the image of S and the image of T if f is a function from A to B and S And T are subsets of A?

Expert Solution

Step 1

Let function f from A into B.

Let S and T are subset of A.

To show that $f (A \cap B) \subset f (A) \cap f (B)$ .

Let $y \in f (A \cap B)$ .

To prove that $y \in f (A) \cap f (B)$ .

$y \in f (A \cap B)$ means that there exist $x \in A \cap B$ such that $f (x) = y$ .

Here, $x \in A \cap B$ implies that $x \in A$ such that $f (x) = y$ and $x \in B$ such that $f (x) = y$ .

That is, $y \in f (A) a n d y \in f (B)$

Implies that $y \in f (A) \cap f (B)$ .

Thus, $f (A \cap B) \subset f (A) \cap f (B)$ .

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