15.1 Inclusion/Exclusion OBJ:  to use the inclusion- exclusion principle to solve counting problems involving intersections and unions of sets.

Slides:

Advertisements

Similar presentations

15.4, 5 Solving Logarithmic Equations OBJ:  To solve a logarithmic equation.

Advertisements

7.5 Inclusion/Exclusion. Definition and Example- 2 sets |A  B| =|A| + |B| - |A ∩ B| Ex1: |A|=9, |B|=11, |A∩B|=5, |A  B| = ?

Prime and Composite Numbers

7.1 Factors and Greatest Common Factors (GCF) CORD Math Mrs. Spitz Fall 2006.

Thinking Mathematically

Prime and Composite Factors: – When 2 or more numbers are multiplied, each number is called a factor of the product Ex) 1 x 5 = 52 x 5 = 10 1 x 10 = 10.

A number is divisible by another number if the quotient is a whole number with no remainder.

Binary Operations.

CSE115/ENGR160 Discrete Mathematics 04/21/11 Ming-Hsuan Yang UC Merced 1.

Lecture 14: Oct 28 Inclusion-Exclusion Principle.

Rational and Irrational Numbers. Rational Number.

Set, Combinatorics, Probability & Number Theory Mathematical Structures for Computer Science Chapter 3 Copyright © 2006 W.H. Freeman & Co.MSCS Slides Set,

Word Problems Using Venn Diagrams

Least Common Multiple (LCM)

Lowest Common Multiple (LCM)

6.5 – Solving Equations with Quadratic Techniques.

Find the set of integers that is greater than 2 and less than 7 Find the set of integers that is greater than 2 or less than 7 How do the use of the words.

2.1, 6.7 Exponential Equations OBJ:  To solve an exponential equation  To solve an exponential equation using properties of rational number exponents.

Finding Factors Section What are factors? Factors are numbers that can be divided evenly into a larger number called a product. Example:1, 2, 3,

3.5 – Solving Systems of Equations in Three Variables.

Honors Chemistry I. Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Binomial Coefficients, Inclusion-exclusion principle

9.3 Addition Rule. The basic rule underlying the calculation of the number of elements in a union or difference or intersection is the addition rule.

Inclusion-Exclusion Selected Exercises Powerpoint Presentation taken from Peter Cappello’s webpage

The Principle of Inclusion-Exclusion

Mutually Exclusive Events OBJ: Find the probability that mutually exclusive and inclusive events occur.

Counting Techniques. L172 Agenda Section 4.1: Counting Basics Sum Rule Product Rule Inclusion-Exclusion.

PSAT MATHEMATICS 9-A Basic Arithmetic Concepts. Set A collection of “things” that have been grouped together in some way. “things” – elements or members.

Science Course Offerings and Sequences. Choices for 9 th Grade CP Biology CP Biology Accelerated Biology Accelerated Biology.

Bartlesville District Science Fair Awards !!!!. Junior Behavioral & Social Sciences.

A Brief Summary for Exam 2 Subject Topics Number theory (sections ) –Prime numbers Definition Relative prime Fundamental theorem of arithmetic.

Lesson 1: Comparing and Ordering Integers. Number Line  Points to the right of the zero (the origin) represent positive numbers. Points to the left of.

What are Integers?? Many situations cannot be represented by whole numbers. You may need negative numbers to show a loss, a temperature below zero, or.

Chapter 2 Equations & Inequalities Algebra 2 Notes Name:________________ Date:_________________.

1 Section 6.5 Inclusion/Exclusion. 2 Finding the number of elements in the union of 2 sets From set theory, we know that the number of elements in the.

Sub. :- Mathematics Divisibility Std. :- 5 th Chapter no. 5.

15.4, 5 Solving Logarithmic Equations OBJ:  To solve a logarithmic equation.

CS Lecture 11 To Exclude Or Not To Exclude? + -

Spring 2016 COMP 2300 Discrete Structures for Computation Donghyun (David) Kim Department of Mathematics and Physics North Carolina Central University.

4-1 Divisibility I CAN use rules to determine the divisibility of numbers.

THE MATHEMATICAL STUDY OF RANDOMNESS. SAMPLE SPACE the collection of all possible outcomes of a chance experiment  Roll a dieS={1,2,3,4,5,6}

 Prime numbers- Numbers that only have two factors (1 and itself)  Ex: 3= 1x3 5=1x5 13=1x13  Composite numbers –Numbers that have more than 2 factors.

Numbers and Operations on Numbers. Numbers can represent quantities, amounts, and positions on a number line. The counting numbers (1, 2, 3, 4, 5…) are.

Bartlesville District Science Fair Awards !!!!. Junior Behavioral & Social Sciences.

#04 In-Class Activity Sieve of Erasthones Prime and Composite #’s.

5.1 Organized Counting with Venn Diagrams. Venn Diagram.

AP Statistics Monday, 09 November 2015 OBJECTIVE TSW investigate the basics of probability. ASSIGNMENTS DUE (wire basket) –WS Counting Principle #1 TODAY’S.

A Π B = all elements in both sets A and B

Least Common Multiple Objective: To find the least common multiple

Chemistry I. Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement.

Learn to use divisibility rules. 4.1 Divisibility.

Principle of Inclusion and Exclusion

Section 5-1 Factoring Numbers

Counting by Complement and the Inclusion/Exclusion Principle

Review of yesterday… How many sig figs are in the following? 0.02

Section 16 Inclusion/Exclusion

To Exclude Or Not To Exclude?

Do Now Solve (-51) = (-47) = = 12 + (-42) =

PRIME AND COMPOSITE NUMBERS

Discrete Math for CS CMPSC 360 LECTURE 27 Last time: Counting.

Set, Combinatorics, Probability & Number Theory

2 Chapter Introduction to Logic and Sets

15.1 Venn Diagrams.

Section 16 Inclusion/Exclusion

Counting Elements of Disjoint Sets: The Addition Rule

What’s on the exam? Sequences and Induction: Ch

Counting Elements of Disjoint Sets: The Addition Rule

To Start: 15 Points Solve the following: 21,672 ÷ 3 = 45,225 ÷ 5 = 210,060 ÷ 10 = 7,224 9,045 21,006.

Multiplication and Division of Integers

Presentation transcript:

15.1 Inclusion/Exclusion OBJ:  to use the inclusion- exclusion principle to solve counting problems involving intersections and unions of sets

DEF:  The Inclusion-Exclusion Principle

EX:  How many positive integers less than 200 are divisible by 3 or 5?

EX:  Of the first 100 positive integers, 25 are prime, 9 are factors of 100, and 68 are neither prime or a factor of 100 How many are: a) both prime and a factor of 100? b) a factor of 100 but not prime?

EX:  Of the 540 seniors at Central High School, 335 are taking mathematics, 287 are taking science, and 220 are taking both mathematics and science. How many are taking neither mathematics nor science?

EX:  Of 150 students who are taking at least one science class, 45 are taking Biology, 75 are taking Chemistry, and 75 are taking Physics. Fifteen students are taking both Chemistry and Physics, 35 are taking only Chemistry, 25 are taking Biology and Chemistry, and no one is taking all three classes. How many students are taking only Biology?