**Mathematical Proof Exercise****Statement:**Let $ A, B, C \subset X $. Then:\[ \text{(a) } A \cap B \subseteq A \text{ and } A \cap B \subseteq B \]**Instructions:**Show the proof.

Answered: Let A. B C+ Then b.1 AnB c A Ond An B…

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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**Mathematical Proof Exercise**

**Statement:**

Let $ A, B, C \subset X $. Then:
\[ \text{(a) } A \cap B \subseteq A \text{ and } A \cap B \subseteq B \]

**Instructions:**

Show the proof.

Expert Solution

Step 1

Note:- in given problem some points are missing you don't define any relation between R and A, B. So, i think by mistake you write R instead of B. If you forget to define any relation between A and B then please resubmit your question with mentioning that. Thank you

Step:- 1

Subset:- A set X is called subset of set Y if every element of X is also in Y that is, whole X is in Y.

Intersection:- Let X and Y be two set then intersection of X and Y is denoted by $A \cap B$ , is the set of all those elements of A and B that are common in A and B.

Case I:- If A and B are empty set that is, A= $\emptyset$ , B= $\emptyset$ and $A \cap B = \emptyset$

then $A \cap B \subseteq A$ and $A \cap B \subseteq B$

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