Explanation Equal sets: The set A and C are said to be an equal set, if and only if the set A have exactly same element as in the set C irrespective of the order of elements. Also, the two sets are said to be equal if and only if A ⊆ C and C ⊆ A . Consider the given sets, A = { a , b , c } B = { x , y } C = { c , a , b } D = { x | 1 ≤ x ≤ 3 and x

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

12th Edition

ISBN: 9780321987297

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 2.2B, Problem 6A

To determine

Whether which of the following sets represents an equal set.

A={a, b, c}

B={x, y}

C={c, a, b}

D={x| 1≤x≤3 and x∈N}

I={x|x=2n and n∈W}

K={2,4,6,8,10,12,…}

L={x|x=2n−1 and n∈N}

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Chapter 2.2B, Problem 5A

Chapter 2.2B, Problem 7A

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One hundred students were surveyed about their preference between dogs and cats. The following two-way table displays data for the sample of students who responded to the survey. Preference Male Female TOTAL Prefers dogs \[36\] \[20\] \[56\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] problem 1 Find the probability that a randomly selected student prefers dogs.Enter your answer as a fraction or decimal. \[P\left(\text{prefers dogs}\right)=\] Incorrect Check Hide explanation Preference Male Female TOTAL Prefers dogs \[\blueD{36}\] \[\blueD{20}\] \[\blueE{56}\] Prefers cats \[10\] \[26\] \[36\] No preference \[2\] \[6\] \[8\] TOTAL \[48\] \[52\] \[100\] There were \[\blueE{56}\] students in the sample who preferred dogs out of \[100\] total students.

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Chapter 2 Solutions

A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)

Ch. 2.1 - Explain why commands and questions are not...Ch. 2.1 - Explain how to write the negation of a quantified...Ch. 2.1 - a. Describe under what conditions a disjunction is...Ch. 2.1 - Consider the nursery rhyme. For want of a nail,...Ch. 2.1 - In an email address line, a coma or a semicolon is...Ch. 2.1 - If a statement and its converse are both true,...Ch. 2.1 - Table 5 shows a situation used to motivate the...Ch. 2.1 - A student in a logic class suggested that one...Ch. 2.1 - Discuss the paradox arising from the following set...Ch. 2.1 - Prob. 10MC

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Whether which of the following sets represents an equal set. A = { a , b , c } B = { x , y } C = { c , a , b } D = { x | 1 ≤ x ≤ 3 and x ∈ N } I = { x | x = 2 n and n ∈ W } K = { 2 , 4 , 6 , 8 , 10 , 12 , … } L = { x | x = 2 n − 1 and n ∈ N }

Solution Summary: The author explains that the set A and C are equal if the two sets have exactly the same element irrespective of the order of elements.

Concept explainers

Whether which of the following sets represents an equal set.

A={a, b, c}

B={x, y}

C={c, a, b}

D={x| 1≤x≤3 and x∈N}

I={x|x=2n and n∈W}

K={2,4,6,8,10,12,…}

L={x|x=2n−1 and n∈N}

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Chapter 2 Solutions

Whether which of the following sets represents an equal set. A = { a , b , c } B = { x , y } C = { c , a , b } D = { x | 1 ≤ x ≤ 3 and x ∈ N } I = { x | x = 2 n and n ∈ W } K = { 2 , 4 , 6 , 8 , 10 , 12 , … } L = { x | x = 2 n − 1 and n ∈ N }

Solution Summary: The author explains that the set A and C are equal if the two sets have exactly the same element irrespective of the order of elements.

Concept explainers

Whether which of the following sets represents an equal set. A={a, b, c} B={x, y} C={c, a, b} D={x| 1≤x≤3 and x∈N} I={x|x=2n and n∈W} K={2,4,6,8,10,12,…} L={x|x=2n−1 and n∈N}

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Chapter 2 Solutions

Whether which of the following sets represents an equal set.

A={a, b, c}

B={x, y}

C={c, a, b}

D={x| 1≤x≤3 and x∈N}

I={x|x=2n and n∈W}

K={2,4,6,8,10,12,…}

L={x|x=2n−1 and n∈N}