   # Prove each statement in 39-44. For every positive integer n , if A 1 , A 2 , A 2 , ....... and B are any sets, then ∪ i = 1 n ( A i − B ) = ( ∪ i = 1 n A i ) − B ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

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

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.2, Problem 41ES
Textbook Problem
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## Prove each statement in 39-44.For every positive integer n, if A 1 , A 2 , A 2 , ....... and B are any sets, then ∪ i = 1 n ( A i − B ) = ( ∪ i = 1 n A i ) − B

To determine

To Prove:

For all integers n1, A1,A2,A3,........ and B are any sets, then

i=1n(AiB)=(i=1nAi)B

### Explanation of Solution

Given information:

Let A and B1,B2,B3,.......,Bn are any sets.

Concept used:

:Union of sets:Intersection of sets

: subset of set

: Null set

Calculation:

If xi=1n(AiB) then xAiB for some i=1,2,..............,n and so, for some i=1,2,..............,n ,

xAi

And xB.

Conversely if x(i=1nAi)B then xi=1nAi

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