/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 2.7 Use Venn diagrams(a) to simplif... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Log out

Learning Materials

Features

Discover

Chapter 2: Q. 2.7 (page 52)

Use Venn diagrams

(a)to simplify the expressions (E∪F)(E∪Fc);

(b)to prove DeMorgan’s laws for eventsEandF. [That is, prove(E∪F)c=EcFc, and (EF)c=Ec∪Fc]

Short Answer

Expert verified

By using the commutative, distributive, and associative properties of(∪,∩)

a)E

b)EF

c)F∪EG

Step by step solution

01

Given Information.

(a)expressions(E∪F)(E∪Fc);

(b)(E∪F)c=EcFc,and(EF)c=Ec∪Fc.

02

Part (a) Explanation.

a) Simplification of (E∪F)E∪Fc

(E∪F)E∪Fc=(E∪F)E∪(E∪F)Fc

=E∪(E∪F)Fc

=E∪EFc∪FFc

=E∪EFc∪FFc

=E∪EFc∪∅

=E∪EFc

=E

03

part (b) Explanation.

b) Simplification of (E∪F)Ec∪FE∪Fc

(E∪F)Ec∪FE∪Fc=(E∪F)E∪FcEc∪F

=(E∪F)E∪FcEc∪F

=EEc∪F

=EEc∪EF

=∅∪EF

=EF

04

part (c) Explanation.

c) Simplification of (E∪F)(F∪G)

(E∪F)(F∪G)=(E∪F)F∪(E∪F)G

=F∪(E∪F)G

=F∪EG∪FG

=F∪FG∪EG

=F∪EG

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A customer visiting the suit department of a certain store will purchase a suit with a probability of.22, a shirt with a probability of.30, and a tie with a probability.28. The customer will purchase both a suit and a shirt with probabilityrole="math" localid="1649314729679" .11, both a suit and a tie with probability.14, and both a shirt and a tie with probability.10. A customer will purchase all3items with a probability of.06. What is the probability that a customer purchases

(a)none of these items?

(b)exactly1of these items?

Suppose that a person chooses a letter at random from R E S E R V E and then chooses one at random from V E R T I C A L. What is the probability that the same letter is chosen?

Suppose that A and B are mutually exclusive events for which P(A)=.3andP(B)=.5. What is the probability that

(a) either A or B occurs?

(b) A occurs but B does not?

(c) both A and B occur?

Five balls are randomly chosen, without replacement, from an urn that contains 5red,6white, and 7blue balls. Find the probability that at least one ball of each color is chosen.

A total of 28 percent of American males smoke cigarettes, 7 percent smoke cigars, and 5 percent smoke both cigars and cigarettes.

(a)What percentage of males smokes neither cigars nor cigarettes?

(b)What percentage smokes cigars but not cigarettes?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.