Explanation Given information: Let A , B and C be 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 Calculation: Let A , B and C be any sets. The objective is to prove that if A ⊆ B and A ⊆ C then A ⊆ B ∩ C To show A ⊆ B ∩ C , it is enough to show that ∀ x , if x ∈ A then x ∈ B ∩ C . Let x ∈ A and A ⊆ B , A ⊆ C

5th Edition

ISBN: 9780357035283

Author: EPP

Publisher: Cengage

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 6.2, Problem 16ES

To determine

To prove:

For all sets A,B and C, if A⊆B and A⊆C then A⊆B∩C.

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Chapter 6.2, Problem 15ES

Chapter 6.2, Problem 17ES

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Chapter 6 Solutions

Discrete Mathematics With Applications

Ch. 6.1 - The notation is read”______” and means that___Ch. 6.1 - To use an element argument for proving that a set...Ch. 6.1 - Prob. 3TY Ch. 6.1 - An element x is in AB if , and only if,_______Ch. 6.1 - An element x in AB if, and only if,______Ch. 6.1 - An element x is in B-A if, and only if,______Ch. 6.1 - An elements x is in Acif, and only if.______Ch. 6.1 - The empty set is a set with ______Ch. 6.1 - The power set of a set A is _____Ch. 6.1 - Prob. 10TY

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To prove: For all sets A , B and C , if A ⊆ B and A ⊆ C then A ⊆ B ∩ C .

Solution Summary: The author concludes that the result Asubseteq Bcap C is true for all sets

Concept explainers

To prove:

For all sets A,B and C, if A⊆B and A⊆C then A⊆B∩C.

Want to see the full answer?

Chapter 6 Solutions

To prove: For all sets A , B and C , if A ⊆ B and A ⊆ C then A ⊆ B ∩ C .

Solution Summary: The author concludes that the result Asubseteq Bcap C is true for all sets

Concept explainers

To prove: For all sets A,B and C, if A⊆B and A⊆C then A⊆B∩C.

Want to see the full answer?

Chapter 6 Solutions

To prove:

For all sets A,B and C, if A⊆B and A⊆C then A⊆B∩C.