2 ∩ A3) A1 ∩ A2 ∩ A3 A1 ∩ A2' ∩ A3' (A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3)   (b) All plants are completed by the contract date. A1 ∪ A2 ∪ A3 A1 ∪ (A2 ∩ A3) (A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3) A1 ∩ A2' ∩ A3' A1 ∩ A2 ∩ A3   (c) Only the plant at site 1 is completed by the contract date. A1 ∪ A2 ∪ A3 (A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3) A1 ∩ A2' ∩ A3' A1 ∪ (A2 ∩ A3) A1 ∩ A2 ∩ A3

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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An engineering construction firm is currently working on power plants at three different sites. Let Ai denote the event that the plant at site i is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1A2, and A3, draw a Venn diagram, and shade the region corresponding to each one.

(a) At least one plant is completed by the contract date.

A1 ∪ A2 ∪ A3
A1 ∪ (A2 ∩ A3)
A1 ∩ A2 ∩ A3
A1 ∩ A2' ∩ A3'
(A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3)
 
(b) All plants are completed by the contract date.
A1 ∪ A2 ∪ A3
A1 ∪ (A2 ∩ A3)
(A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3)
A1 ∩ A2' ∩ A3'
A1 ∩ A2 ∩ A3
 
(c) Only the plant at site 1 is completed by the contract date.
A1 ∪ A2 ∪ A3
(A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3)
A1 ∩ A2' ∩ A3'
A1 ∪ (A2 ∩ A3)
A1 ∩ A2 ∩ A3
 
(d) Exactly one plant is completed by the contract date.
A1 ∩ A2' ∩ A3'
(A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3)
A1 ∪ (A2 ∩ A3)
A1 ∪ A2 ∪ A3
A1 ∩ A2 ∩ A3
(e) Either the plant at site 1 or both of the other plants are completed by the contract date.
A1 ∩ A2' ∩ A3'
(A1 ∩ A2' ∩ A3') ∪ (A1' ∩ A2 ∩ A3') ∪ (A1' ∩ A2' ∩ A3)
A1 ∪ A2 ∪ A3
A1 ∪ (A2 ∩ A3)
A1 ∩ A2 ∩ A3
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