   Chapter 9.8, Problem 12ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Prove that if S is any sample space and U and V are any events in S, then P ( V − U ) = P ( V ) − P ( U ∩ V ) .

To determine

Proof of the given statement.

Explanation

Given information:

A sample space S and events U and V such that UV.

Calculation:

Since for all sets U and V ,

U(VU)=UV

Apply probabilities both sides.

P(U(VU))=P(UV)

Since, U and (VU) are disjoint sets.

By the probability axiom 3 ,

p(AB)=p(A)+p(B) if both A,B are mutually exclusive events

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