MATH 210: DISCRETE MATH

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MATH 210 DISCRETE MATH

• Textbook A Discrete Math Primer
• by Kathleen M.
  Shannon
• Homework Supplement on the web pages.

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Dr. Philip E. Luft

• On-campus email Philip Luft
• Off-campus email peluft_at_salisbury.edu
• Office Telephone [phone]
• Office Hours in HS 126
• See my Schedule on the web.
• http//faculty.salisbury.edu/peluft/210/

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FIND ME ON THE WEB

• NETWARE APPLICATION LAUNCHER
• NETSCAPE
• http//faculty.salisbury.edu/peluft/210/
• PRINT GRADING, POLICIES, HOMEWORK
• READ AND FOLLOW THE POLICIES

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MATH 210 DISCRETE MATH

• FOR MATH MAJORS
• REQUIRES FINDING INFO IN BOOK
• Use the index of terms on the web.
• USES DEFINITIONS PRECISELY
• EMPHASIZES PROOF
• PREP FOR MOST 400 LEVEL COURSES

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QUIZZES

• EVERY DAY except when a test is returned
• ONE OR MORE HOMEWORK PROBLEMS
• AFTER THE FIRST 20 QUIZZES,
• THE REST ARE MAKEUPS.
• NO MAKEUP QUIZZES OUTSIDE CLASS

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I MAY CALL ON YOUYOU MAY

• ANSWER
• SAY I DONT KNOW
• SAY I PASS

I hope you will learn from the experience, but I
will not grade you.
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EXTRA CREDIT

• PRESENT A SOLUTION AT REVIEW
• MAKE COPIES FOR ALL
• FOLLOW RULES IN THE POLICIES

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1.0 Sets of Numbers

• N the set of natural numbers (counting
  numbers)
• J the set of whole numbers (integers)
• E the set of even natural numbers 2n
• D the set of odd natural numbers 2n-1
• Q the set of rational numbers i / j
• R the set of real numbers (points on the line)

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1.0.2-3 Unions and Intersections

• Let X, Y be any two sets.
• X?Y is the set of all elements of either X or Y
  (or both)
• X?Y is the set of all elements of both X and Y

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1.0.5 Difference of Sets

• Let X, Y be any sets. Then
• X-Y set of elements in X but not in Y

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1.0.7 Subsets

• X?Y means every element of X is an element of Y
  (Perhaps XY)
• If X?Y and at least one element of Y is not in X,
  then we can also write X?Y
• We understand Y?X to mean X?Y and
• We understand Y?X to mean X?Y

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1.1.0 Set Equality

• Let X, Y be any sets. Then
• X Y means that X, Y have the same elements
  (though perhaps X, Y are described differently).
• X Y is logically equivalent to the
  simultaneous truth of the statements X ? Y and X
  ? Y .
• Proof requires using the contrapositive

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End Lesson 1a
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SET EQUALITY

• VENN DIAGRAMS
• TRUTH TABLES
• ELEMENT CHASING

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1.0.6 Venn Diagrams

• a)
• (X ? Y) ? Z (X ? Z) ? (Y ? Z)
• c)
• (X ? Y ? Z) ? (X ? Y ? Z)'
• (X ? (Y' ? Z')) ? (Y ? (X' ? Z')) ? (Z ? (X' ?
  Y'))
• (Analyzed in Primer)

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1.2.1f Set Identities by Truth Table Y ? (X
? Y) Y

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1.2.1j Set Identities by Truth Table X ?
(X' ? Y) X ? Y

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Alternative to 1.1.2 Truth Table (X ? Y) ? (X ?
Y)' (X ? Y') ? (Y ? X')

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1.1.2a Truth Table for Three Sets (X ? Y) ? Z
(X ? Z) ? (Y ? Z)

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1.1.2 Truth Tables / Element Chasing

• a)
• (X ? Y) ? Z (X ? Z) ? (Y ? Z)
• c)
• (X ? Y ? Z) ? (X ? Y ? Z)'
• (X ? (Y' ? Z')) ? (Y ? (X' ? Z')) ? (Z ? (X' ?
  Y'))
• (Analyzed in Primer)

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MATHEMATICAL SYMBOLS

• ? ? ? ? ? ? ? ? ?
• ? ? ? ? ? ?
• ? ? ? ? ? ? ?
• ? ? ? ? ?

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1.1.2 Truth Table for Two Sets

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1.1.2 Truth Table for Three Sets