MATH W/APPLICATIONS W/ACCESS
12th Edition
ISBN: 9780135335215
Author: Lial
Publisher: PEARSON
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Chapter 8.5, Problem 1CP
✓ Checkpoint 1
Use the date in the table to find
a.
b.
c.
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Determine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}. f: Z_(6) -> Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) -> Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z -> Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).
Determine whether each function is an injection and determine whether each is a surjection.
Let A
=
{a, b, c, d}, B = {a,b,c}, and C = {s, t, u,v}. Draw an arrow diagram of a function
for each of the following descriptions. If no such function exists, briefly explain why.
(a) A function f : AC whose range is the set C.
(b) A function g: BC whose range is the set C.
(c) A function g: BC that is injective.
(d) A function j : A → C that is not bijective.
Chapter 8 Solutions
MATH W/APPLICATIONS W/ACCESS
Ch. 8.1 - Checkpoint 1
Indicate whether each statement is...Ch. 8.1 - Prob. 2CPCh. 8.1 - Prob. 3CPCh. 8.1 - Prob. 4CPCh. 8.1 - Checkpoint 5
Find the number of subsets for each...Ch. 8.1 - Prob. 6CPCh. 8.1 - Prob. 7CPCh. 8.1 - Prob. 8CPCh. 8.1 - Prob. 9CPCh. 8.1 - Prob. 10CP
Ch. 8.1 - Write true or false for each statement. (See...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - Write true or false for each statement. (See...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - Prob. 11ECh. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - Prob. 19ECh. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - Find the number of subsets of the given set. (See...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Insert or to make each statement true. (See...Ch. 8.1 - Prob. 30ECh. 8.1 - Insert or to make each statement true. (See...Ch. 8.1 - Insert or to make each statement true. (See...Ch. 8.1 - Insert or to make each statement true. (See...Ch. 8.1 - Insert or to make each statement true. (See...Ch. 8.1 - Insert or to make each statement true. (See...Ch. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - Prob. 39ECh. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Prob. 53ECh. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Food and Drink Sales Sales (in millions of...Ch. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.1 - Prob. 65ECh. 8.1 - Prob. 66ECh. 8.1 - Prob. 67ECh. 8.1 - Prob. 68ECh. 8.1 - Prob. 69ECh. 8.1 - Prob. 70ECh. 8.1 - Prob. 71ECh. 8.1 - Prob. 72ECh. 8.1 - Prob. 73ECh. 8.1 - Prob. 74ECh. 8.1 - Prob. 75ECh. 8.1 - Prob. 76ECh. 8.1 - Prob. 77ECh. 8.1 - Farm Products The following table gives the amount...Ch. 8.2 - Checkpoint 1
Draw Venn diagrams for the given set...Ch. 8.2 - Prob. 2CPCh. 8.2 - Checkpoint 3
(a) Place numbers in the regions on a...Ch. 8.2 - Prob. 4CPCh. 8.2 - Checkpoint 5
In example 5, suppose 75 patients...Ch. 8.2 - Prob. 6CPCh. 8.2 - Prob. 7CPCh. 8.2 - Sketch a Venn diagram like the one shown, and use...Ch. 8.2 - Prob. 2ECh. 8.2 - Prob. 3ECh. 8.2 - Prob. 4ECh. 8.2 - Prob. 5ECh. 8.2 - Prob. 6ECh. 8.2 - Prob. 7ECh. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Prob. 11ECh. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - Use Venn diagrams to answer the given questions....Ch. 8.2 - Use Venn diagrams to answer the given questions....Ch. 8.2 - 19. Business The human resources director for a...Ch. 8.2 - 20. Business A pet store keeps track of the...Ch. 8.2 - 21. Natural Science A marine biologist surveys...Ch. 8.2 - 22. Health Human blood can contain either no...Ch. 8.2 - 23. Natural Science Use the diagram from Exercise...Ch. 8.2 - 24. Business In reviewing the portfolios of 365 of...Ch. 8.2 - For Exercises 25-30, use the given contingency...Ch. 8.2 - For Exercises 25-30, use the given contingency...Ch. 8.2 - Life Classification In Exercises 27 and 28, the...Ch. 8.2 - Life Classification In Exercises 27 and 28, the...Ch. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Prob. 31ECh. 8.2 - Prob. 32ECh. 8.2 - Prob. 33ECh. 8.2 - 30. If n(A) =5, n(B) = 8, and n( A ∩ B) = 4, what...Ch. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Prob. 39ECh. 8.2 - Prob. 40ECh. 8.2 - Prob. 41ECh. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - Prob. 46ECh. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.3 - Checkpoint 1
Draw a tree diagram for the random...Ch. 8.3 - Checkpoint 2
Suppose a die is tossed. Write the...Ch. 8.3 - Checkpoint 3
Which of the events listed in...Ch. 8.3 - Checkpoint 4
Write the set notation for the given...Ch. 8.3 - Checkpoint 5
In Example 5, let F = {2, 4, 6}, K =...Ch. 8.3 - Checkpoint 6
A fair die is rolled. Find the...Ch. 8.3 - Checkpoint 7
A single playing card is drawn at...Ch. 8.3 - Checkpoint 8
From the data given in Example 8,...Ch. 8.3 - 1. What is meant by a “fair” coin or die?
Ch. 8.3 - 2. What is the sample space for a random...Ch. 8.3 - 3. A month of the year is chosen for a...Ch. 8.3 - Write sample spaces for the random experiments in...Ch. 8.3 - Write sample spaces for the random experiments in...Ch. 8.3 - Write sample spaces for the random experiments in...Ch. 8.3 - Write sample spaces for the random experiments in...Ch. 8.3 - Write sample spaces for the random experiments in...Ch. 8.3 - Write sample spaces for the random experiments in...Ch. 8.3 - 10. Define an event.
Ch. 8.3 - 11. Define disjoint events in your own words.
Ch. 8.3 - Decide whether the events are disjoint. (See...Ch. 8.3 - Decide whether the events are disjoint. (See...Ch. 8.3 - Decide whether the events are disjoint. (See...Ch. 8.3 - Decide whether the events are disjoint. (See...Ch. 8.3 - Decide whether the events are disjoint. (See...Ch. 8.3 - Decide whether the events are disjoint. (See...Ch. 8.3 - For the random experiments in Exercises 18–20,...Ch. 8.3 -
For the random experiments in Exercises 18–20,...Ch. 8.3 - For the random experiments in Exercises 18–20,...Ch. 8.3 - In Exercises 21–23, write out the sample space and...Ch. 8.3 - In Exercises 21–23, write out the sample space and...Ch. 8.3 - In Exercises 21–23, write out the sample space and...Ch. 8.3 - Prob. 24ECh. 8.3 - Prob. 25ECh. 8.3 - A single fair die is rolled. Find the...Ch. 8.3 - A single fair die is rolled. Find the...Ch. 8.3 - A single fair die is rolled. Find the...Ch. 8.3 - David Klein wants to adopt a puppy from an animal...Ch. 8.3 - Prob. 30ECh. 8.3 - Prob. 31ECh. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Prob. 34ECh. 8.3 - Prob. 35ECh. 8.3 - Prob. 36ECh. 8.3 - Business The following table gives the number of...Ch. 8.3 - Business The following table gives the number of...Ch. 8.3 - 39. Social Science Respondents to the 2012 General...Ch. 8.3 - Prob. 40ECh. 8.3 - S&P 500 As of March 7, 2017, the 505 stocks in the...Ch. 8.3 - SP 500 As of March 7, 2017, the 505 stocks in the...Ch. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.3 - Prob. 52ECh. 8.4 - Checkpoint 1
If an American roulette wheel is...Ch. 8.4 - Checkpoint 2
In the random experiment of Example...Ch. 8.4 - Prob. 3CPCh. 8.4 - Checkpoint 4
(a) Let Find
(b) If find
Ch. 8.4 - Prob. 5CPCh. 8.4 - Prob. 6CPCh. 8.4 - Prob. 7CPCh. 8.4 - Prob. 8CPCh. 8.4 - Prob. 9CPCh. 8.4 - Assume a single spin of the roulette wheel is...Ch. 8.4 - Assume a single spin of the roulette wheel is...Ch. 8.4 - Assume a single spin of the roulette wheel is...Ch. 8.4 - Also with a single spin of the roulette wheel,...Ch. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - Prob. 9ECh. 8.4 - Prob. 10ECh. 8.4 - Two dice are rolled. Find the probabilities of...Ch. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Tami goes shopping and sees three kinds of shoes:...Ch. 8.4 - Ms. Elliott invites 10 relatives to a party: her...Ch. 8.4 - Prob. 16ECh. 8.4 - Use Venn diagrams to work Exercises 17–21. (See...Ch. 8.4 - Prob. 18ECh. 8.4 - Use Venn diagrams to work Exercises 17–22. (See...Ch. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - Prob. 27ECh. 8.4 - 28. Find the odds of not drawing a white marble in...Ch. 8.4 - Prob. 29ECh. 8.4 - Prob. 30ECh. 8.4 - Prob. 31ECh. 8.4 - Education For Exercises 31–34, find the odds of...Ch. 8.4 - Prob. 33ECh. 8.4 - Prob. 34ECh. 8.4 - Government Revenue For Exercises 3538, convert the...Ch. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Government Revenue For Exercises 3538, convert the...Ch. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - S&P 500 Stocks For Exercises 39–46, use the...Ch. 8.4 - Prob. 42ECh. 8.4 - One way to solve a probability problem is to...Ch. 8.4 - One way to solve a probability problem is to...Ch. 8.4 - One way to solve a probability problem is to...Ch. 8.4 - Prob. 58ECh. 8.4 - SP 500 Stocks For Exercises 3946, use the...Ch. 8.4 - SP 500 Stocks For Exercises 3946, use the...Ch. 8.4 - Prob. 45ECh. 8.4 - S&P 500 Stocks For Exercises 39–46, use the...Ch. 8.4 - Hours Worked Data from the 2016 General Social...Ch. 8.4 - Hours Worked Data from the 2016 General Social...Ch. 8.4 - Hours Worked Data from the 2016 General Social...Ch. 8.4 - Hours Worked Data from the 2016 General Social...Ch. 8.4 - Hours Worked Data from the 2016 General Social...Ch. 8.4 - Hours Worked Data from the 2016 General Social...Ch. 8.4 - Hours Worked Data from the 2016 General Social...Ch. 8.4 - Prob. 54ECh. 8.4 - Prob. 59ECh. 8.4 - Prob. 60ECh. 8.5 - ✓ Checkpoint 1
Use the date in the table to...Ch. 8.5 - Prob. 2CPCh. 8.5 - Prob. 3CPCh. 8.5 - Checkpoint 4
In Example 3, find the probability...Ch. 8.5 - Prob. 5CPCh. 8.5 - Prob. 6CPCh. 8.5 - Prob. 7CPCh. 8.5 - Prob. 8CPCh. 8.5 - Prob. 9CPCh. 8.5 - Prob. 10CPCh. 8.5 - Prob. 11CPCh. 8.5 - Prob. 12CPCh. 8.5 - If a single fair die is rolled, find the...Ch. 8.5 - If a single fair die is rolled, find the...Ch. 8.5 - If a single fair die is rolled, find the...Ch. 8.5 - Prob. 4ECh. 8.5 - If two fair dice are rolled (recall the 36-outcome...Ch. 8.5 - If two fair dice are rolled (recall the 36-outcome...Ch. 8.5 - If two cards are drawn without replacement from an...Ch. 8.5 - Prob. 8ECh. 8.5 - If two cards are drawn without replacement from an...Ch. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - 14. A student reasons that the probability in...Ch. 8.5 - Decide whether the two events listed are...Ch. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Decide whether the two events listed are...Ch. 8.5 - Decide whether the two events listed are...Ch. 8.5 - Firm Size According to data from the U.S. Small...Ch. 8.5 - Prob. 22ECh. 8.5 - Firm Size According to data from the U.S. Small...Ch. 8.5 - Firm Size According to data from the U.S. Small...Ch. 8.5 - Hours Worked Data from the 2016 General Social...Ch. 8.5 - Hours Worked Data from the 2016 General Social...Ch. 8.5 - Hours Worked Data from the 2016 General Social...Ch. 8.5 - Prob. 28ECh. 8.5 - Hours Worked Data from the 2016 General Social...Ch. 8.5 - Prob. 31ECh. 8.5 - Prob. 30ECh. 8.5 - Prob. 32ECh. 8.5 - Prob. 33ECh. 8.5 - Prob. 34ECh. 8.5 - Natural Science The following table shows...Ch. 8.5 - Prob. 36ECh. 8.5 - Natural Science The following table shows...Ch. 8.5 - Natural Science The following table shows...Ch. 8.5 - Natural Science The following table shows...Ch. 8.5 - Prob. 40ECh. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Prob. 44ECh. 8.5 - Social Science The Motor Vehicle Department in a...Ch. 8.5 - Social Science The Motor Vehicle Department in a...Ch. 8.5 - Prob. 47ECh. 8.5 - Prob. 48ECh. 8.5 - Prob. 49ECh. 8.5 - Prob. 50ECh. 8.5 - Prob. 51ECh. 8.5 - Prob. 52ECh. 8.5 - Prob. 53ECh. 8.5 - Prob. 54ECh. 8.5 - Prob. 55ECh. 8.5 - Prob. 56ECh. 8.5 - Prob. 57ECh. 8.5 - Prob. 58ECh. 8.5 - Prob. 59ECh. 8.5 - Prob. 60ECh. 8.5 - Prob. 61ECh. 8.5 - Prob. 62ECh. 8.5 - Prob. 63ECh. 8.5 - Prob. 64ECh. 8.6 - Prob. 1CPCh. 8.6 - Prob. 2CPCh. 8.6 - Prob. 3CPCh. 8.6 - Prob. 4CPCh. 8.6 - Prob. 1ECh. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - Prob. 5ECh. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - S&P 500 Stocks On March 7, 2017, the probability...Ch. 8.6 - Prob. 10ECh. 8.6 - Prob. 11ECh. 8.6 - Prob. 12ECh. 8.6 - Economics Data from the Bureau of Labor Statistics...Ch. 8.6 - Prob. 14ECh. 8.6 - Prob. 15ECh. 8.6 - Prob. 16ECh. 8.6 - Prob. 17ECh. 8.6 - Prob. 18ECh. 8.6 - Prob. 19ECh. 8.6 - Prob. 20ECh. 8.6 - Prob. 21ECh. 8.6 - Prob. 22ECh. 8.6 - Prob. 23ECh. 8.6 - Prob. 24ECh. 8.6 - Business At the close of the markets on May 19,...Ch. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - Prob. 28ECh. 8.6 - Prob. 29ECh. 8.6 - Prob. 30ECh. 8.6 - Prob. 31ECh. 8.6 - Prob. 32ECh. 8.6 - Prob. 33ECh. 8.6 - Prob. 34ECh. 8.6 - Prob. 35ECh. 8.6 - Prob. 36ECh. 8 - Prob. 1RECh. 8 - Write true or false for each of the given...Ch. 8 - Write true or false for each of the given...Ch. 8 - Write true or false for each of the given...Ch. 8 - Write true or false for each of the given...Ch. 8 - Write true or false for each of the given...Ch. 8 - Write true or false for each of the given...Ch. 8 - Write true or false for each of the given...Ch. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - List the elements in the given sets. { xx is a...Ch. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - Prob. 20RECh. 8 - Prob. 21RECh. 8 - Prob. 22RECh. 8 - Prob. 23RECh. 8 - Draw a Venn diagram and shade the given set in...Ch. 8 - Prob. 25RECh. 8 - Prob. 26RECh. 8 - Prob. 27RECh. 8 - Prob. 28RECh. 8 - Prob. 29RECh. 8 - Prob. 30RECh. 8 - Prob. 31RECh. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RECh. 8 - Prob. 36RECh. 8 - Prob. 37RECh. 8 - Prob. 38RECh. 8 - Prob. 39RECh. 8 - Prob. 40RECh. 8 - Prob. 41RECh. 8 - Prob. 42RECh. 8 - Prob. 43RECh. 8 - Prob. 44RECh. 8 - Prob. 45RECh. 8 - Prob. 46RECh. 8 - Prob. 47RECh. 8 - Prob. 48RECh. 8 - Prob. 49RECh. 8 - Prob. 50RECh. 8 - Prob. 51RECh. 8 - Prob. 52RECh. 8 - Confidence in Major Corporations The following...Ch. 8 - Prob. 54RECh. 8 - Confidence in Major Corporations The following...Ch. 8 - Prob. 56RECh. 8 - Prob. 57RECh. 8 - Prob. 58RECh. 8 - Prob. 59RECh. 8 - Prob. 60RECh. 8 - Prob. 61RECh. 8 - Prob. 62RECh. 8 - Prob. 63RECh. 8 - Prob. 64RECh. 8 - Prob. 65RECh. 8 - Prob. 66RECh. 8 - Prob. 67RECh. 8 - Prob. 68RECh. 8 - Prob. 69RECh. 8 - Prob. 70RECh. 8 - Prob. 71RECh. 8 - Prob. 72RECh. 8 - Prob. 73RECh. 8 - Prob. 74RECh. 8 - Prob. 75RECh. 8 - Prob. 76RECh. 8 - Prob. 77RECh. 8 - Prob. 78RECh. 8 - Give examples. Stock Market Performance On May 12,...Ch. 8 - Prob. 80RECh. 8 - Prob. 81RECh. 8 - Give examples. Stock Market Performance On May 18,...Ch. 8 - Prob. 83RECh. 8 - Prob. 84RECh. 8 - Prob. 85RECh. 8 - Prob. 86RECh. 8 - Prob. 87RECh. 8 - Prob. 88RECh. 8 - Prob. 89RECh. 8 - Prob. 90RECh. 8 - Prob. 91RECh. 8 - Prob. 92RECh. 8 - Social Science The following tables list the...Ch. 8 - Prob. 94RECh. 8 - 91. Are the events “third-class survival” and...Ch. 8 - 92. Are the events “first-class survival” and...Ch. 8 - Prob. 1CECh. 8 - 2. If the sensitivity of a test for a disease is...Ch. 8 - Prob. 3CECh. 8 - Prob. EP
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Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
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ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
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ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Glencoe Algebra 1, Student Edition, 9780079039897...
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Author:Carter
Publisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
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Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY