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
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
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 A1, A2, 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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