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

5th Edition

ISBN: 9781337694193

Author: EPP, Susanna S.

Publisher: Cengage Learning,

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Chapter 6.2, Problem 41ES

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To Prove:

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

∪i=1n(Ai−B)=(∪i=1nAi)−B

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Chapter 6.2, Problem 40ES

Chapter 6.2, Problem 42ES

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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

Solution Summary: The author demonstrates that nge 1,A1,A2,A3,mathrm........ and B are any sets.

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To Prove:

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

∪i=1n(Ai−B)=(∪i=1nAi)−B

Want to see the full answer?

Chapter 6 Solutions

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

Solution Summary: The author demonstrates that nge 1,A1,A2,A3,mathrm........ and B are any sets.

Concept explainers

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To Prove: For all integers n≥1, A1,A2,A3,........ and B are any sets, then ∪i=1n(Ai−B)=(∪i=1nAi)−B

Want to see the full answer?

Chapter 6 Solutions

To Prove:

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

∪i=1n(Ai−B)=(∪i=1nAi)−B