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

Q: Expert Answer

To determine To Prove: For all integers n ≥ 1 , A 1 , A 2 , A 3 , ........ and B are any sets, then ∪ i = 1 n ( A i − B ) = ( ∪ i = 1 n A i ) − B Explanation Given information: Let A and B 1 , B 2 , B 3 , ....... , B n are any sets. Concept used: ∪ : U n i o n of sets ∩ : I n t e r sec t i o n of sets ⊆ : subset of set ∅ : Null set Calculation: If x ∈ ∪ i = 1 n ( A i − B ) then x ∈ A i − B for some i = 1 , 2 , .............. , n and so, for some i = 1 , 2 , .............. , n , x ∈ A i And x ∉ B . Conversely if x ∈ ( ∪ i = 1 n A i ) − B then x ∈ ∪ i = 1 n A i

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Answer 1

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Discrete Mathematics With Applicat...

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BuyFind

Discrete Mathematics With Applicat...

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Solutions

Chapter

Section

Answer 3

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Chapter

Section

Answer 4

Chapter

Section

Answer 5

To determine

To Prove:

For all integers n≥1, A1,A2,A3,........ and B are any sets, then

∪i=1n(Ai−B)=(∪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 x∈∪i=1n(Ai−B) then x∈Ai−B for some i=1,2,..............,n and so, for some i=1,2,..............,n ,

x∈Ai

And x∉B.

Conversely if x∈(∪i=1nAi)−B then x∈∪i=1nAi

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...

Solutions

Discrete Mathematics With Applicat...