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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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For each of 1-4 find a counterexample to show that the statement is false. Assume all sets are subsets of a universal set U.
For all sets A,B, and C, if B C A then
( A B ) ( A C ) = .

To determine

For all sets A,B and C,if BCA then

(AB)(AC)=ϕ.

Explanation

Given information:

Let  A,B and C  be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

For each find a counterexample to show that the statement ¡s false. Assume all sets are subsets of a universal set U.

Exercise

For all sets A,B and C,if BCA then

(AB)(AC)=ϕ.

Consider the statement as.

“For all sets A,B and C,if BCA then (AB)(AC)=ϕ ”.

The objective is to find a counter example to show that the above statement is false.

Consider that all sets are subsets of a universal set U.

Counterexample:

Let U be a universal set defined as,

U={1,2,3,4,5,6}.

Suppose for some sets A and B defined as,

A={1,4},B={1,2,3} and C={1,5,6}.

BC={1,2,3}{1,5,6}={1}A

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Sect-6.1 P-11TYSect-6.1 P-1ESSect-6.1 P-2ESSect-6.1 P-3ESSect-6.1 P-4ESSect-6.1 P-5ESSect-6.1 P-6ESSect-6.1 P-7ESSect-6.1 P-8ESSect-6.1 P-9ESSect-6.1 P-10ESSect-6.1 P-11ESSect-6.1 P-12ESSect-6.1 P-13ESSect-6.1 P-14ESSect-6.1 P-15ESSect-6.1 P-16ESSect-6.1 P-17ESSect-6.1 P-18ESSect-6.1 P-19ESSect-6.1 P-20ESSect-6.1 P-21ESSect-6.1 P-22ESSect-6.1 P-23ESSect-6.1 P-24ESSect-6.1 P-25ESSect-6.1 P-26ESSect-6.1 P-27ESSect-6.1 P-28ESSect-6.1 P-29ESSect-6.1 P-30ESSect-6.1 P-31ESSect-6.1 P-32ESSect-6.1 P-33ESSect-6.1 P-34ESSect-6.1 P-35ESSect-6.1 P-36ESSect-6.1 P-37ESSect-6.1 P-38ESSect-6.2 P-1TYSect-6.2 P-2TYSect-6.2 P-3TYSect-6.2 P-4TYSect-6.2 P-5TYSect-6.2 P-6TYSect-6.2 P-1ESSect-6.2 P-2ESSect-6.2 P-3ESSect-6.2 P-4ESSect-6.2 P-5ESSect-6.2 P-6ESSect-6.2 P-7ESSect-6.2 P-8ESSect-6.2 P-9ESSect-6.2 P-10ESSect-6.2 P-11ESSect-6.2 P-12ESSect-6.2 P-13ESSect-6.2 P-14ESSect-6.2 P-15ESSect-6.2 P-16ESSect-6.2 P-17ESSect-6.2 P-18ESSect-6.2 P-19ESSect-6.2 P-20ESSect-6.2 P-21ESSect-6.2 P-22ESSect-6.2 P-23ESSect-6.2 P-24ESSect-6.2 P-25ESSect-6.2 P-26ESSect-6.2 P-27ESSect-6.2 P-28ESSect-6.2 P-29ESSect-6.2 P-30ESSect-6.2 P-31ESSect-6.2 P-32ESSect-6.2 P-33ESSect-6.2 P-34ESSect-6.2 P-35ESSect-6.2 P-36ESSect-6.2 P-37ESSect-6.2 P-38ESSect-6.2 P-39ESSect-6.2 P-40ESSect-6.2 P-41ESSect-6.2 P-42ESSect-6.2 P-43ESSect-6.2 P-44ESSect-6.3 P-1TYSect-6.3 P-2TYSect-6.3 P-3TYSect-6.3 P-1ESSect-6.3 P-2ESSect-6.3 P-3ESSect-6.3 P-4ESSect-6.3 P-5ESSect-6.3 P-6ESSect-6.3 P-7ESSect-6.3 P-8ESSect-6.3 P-9ESSect-6.3 P-10ESSect-6.3 P-11ESSect-6.3 P-12ESSect-6.3 P-13ESSect-6.3 P-14ESSect-6.3 P-15ESSect-6.3 P-16ESSect-6.3 P-17ESSect-6.3 P-18ESSect-6.3 P-19ESSect-6.3 P-20ESSect-6.3 P-21ESSect-6.3 P-22ESSect-6.3 P-23ESSect-6.3 P-24ESSect-6.3 P-25ESSect-6.3 P-26ESSect-6.3 P-27ESSect-6.3 P-28ESSect-6.3 P-29ESSect-6.3 P-30ESSect-6.3 P-31ESSect-6.3 P-32ESSect-6.3 P-33ESSect-6.3 P-34ESSect-6.3 P-35ESSect-6.3 P-36ESSect-6.3 P-37ESSect-6.3 P-38ESSect-6.3 P-39ESSect-6.3 P-40ESSect-6.3 P-41ESSect-6.3 P-42ESSect-6.3 P-43ESSect-6.3 P-44ESSect-6.3 P-45ESSect-6.3 P-46ESSect-6.3 P-47ESSect-6.3 P-48ESSect-6.3 P-49ESSect-6.3 P-50ESSect-6.3 P-51ESSect-6.3 P-52ESSect-6.3 P-53ESSect-6.3 P-54ESSect-6.4 P-1TYSect-6.4 P-2TYSect-6.4 P-3TYSect-6.4 P-1ESSect-6.4 P-2ESSect-6.4 P-3ESSect-6.4 P-4ESSect-6.4 P-5ESSect-6.4 P-6ESSect-6.4 P-7ESSect-6.4 P-8ESSect-6.4 P-9ESSect-6.4 P-10ESSect-6.4 P-11ESSect-6.4 P-12ESSect-6.4 P-13ESSect-6.4 P-14ESSect-6.4 P-15ESSect-6.4 P-16ESSect-6.4 P-17ESSect-6.4 P-18ESSect-6.4 P-19ESSect-6.4 P-20ESSect-6.4 P-21ESSect-6.4 P-22ESSect-6.4 P-23ESSect-6.4 P-24ESSect-6.4 P-25ESSect-6.4 P-26ESSect-6.4 P-27ESSect-6.4 P-28ESSect-6.4 P-29ES