   # Let A 1 = { 1 } , A 2 = { u , v } , and A 3 = { m , n } . Find each of the following sets: A ∪ ( A 2 × A 3 ) ( A 1 ∪ A 2 ) × A 3 ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193
Chapter 6.1, Problem 34ES
Textbook Problem
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## Let A 1 = { 1 } , A 2 = { u , v } ,   and   A 3 = { m , n } . Find each of the following sets: A ∪ ( A 2 × A 3 ) ( A 1 ∪ A 2 ) × A 3

To determine

(a)

Find

A1×(A2×A3)

### Explanation of Solution

Given information:

A1={1,2,3},A2={u,v} and A3={m,n}

Concept used:

A×B={(a,b)|aA and bB}

Calculation:

Evaluate A1×(A2×A3).

First find the product A2×A3.

A2×A3={(u,m),(u,n),(v,m),(v,n)}

Now,

A1×(A2×A3)={(p,q)|pA1 and q(A2×A3)}

A1×(A2×A3)=[(1,( u,m)),(2,( u,m)),(3( u,m)),(1,( u,n)),(2( u,n))

To determine

(b)

Find the value of

(A1×A2)×A3

To determine

(c)

Find the value of

A1×A2×A3

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