   Chapter 6.3, Problem 10ES ### 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

# For each of 5-21 prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.For all sets A and B, If A ⊆ B then A ∩ B e = ∅ .

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A and B,if AB then ABc=ϕ.

Explanation

Given information:

Let  A,B   be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

Consider the statement,

If AB then ABc=

The objective is to verify whether the statement ¡s true or not.

Recall, the definition for Unions, and, Intersections.

Suppose A and B are two subsets of a universal set U.

1. For a set A to be a subset of a set B is denoted by AB, and is defined by AB;{x, if xA then xB}.
2. The complement of A is denoted by Ac and is defined by

Ac={xU|xA}.

The intersection of A and B, is denoted by AB, and is defined by AB={xU|xA and xB}

Prove that whether the statement is true or false as,

Let A,B be any sets and given that AB

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