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6001210-3Discrete Mathematics

Lecture1

Miss.Amal Alshardy

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Instruction

Kenneth H. Rosen. Discrete Mathematics and Its Applications,

6th Edition

Exams: 2 tests (40%), final (40%)

Homework (10%): equally divided between several assignments.

HW submitted late will not be graded.

Cheating HW will not be graded

Class attendance(10%)

Each class slid should be with you.

Textbook:

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Propositional Logic Truth values, truth tables

Conjunction () Negation () Disjunction () Implication () Biconditional () Exclusive OR()

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Propositions• Declarative sentence(sentence that

declares a fact)• Must be either True or False.Propositions: • UQU is in Makkah (T)• 1+1=2 (T)• 2+2=3 (F)• jeddah is capital of Saudi Arabia (F)

Not propositions:• Do you like this class?• Read this carrfully• X+1=2

Are not declares a fact

Are not declares a fact

They are neither true nor false

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cont. Propositions

• Truth value: True or False

• proposition Variables: Variables that represent proposition..

• We will use letters to denote proposition Variables: p,q,r,s,…

• Negation:p (“not p”)

• Truth table for

• negation

p p

T F

F T

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cont. negating propositions

p: “is the opposite of the truth value of p”

p: “it is not the case that p”

p: “it rained more than 20 inches in TO”

p: “John has many iPads”

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Find the negation of

this two proposition

Conjunction: p q [“and”]

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p q p q

T T T

T F F

F T F

F F F

e.gp: It is snowingq: It is below

freezing

N propositions2N possibility

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Disjunction: p q [“or”]

p q p q

T T T

T F T

F T T

F F F

e.gp: It is snowingq: It is below

freezing

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Exclusive OR (XOR)• p q – T if p and q have different truth

values, F otherwise

p q p q

T T F

T F T

F T T

F F F

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Conditional:p q [“if p then q”]

• p: hypothesis, q: conclusion• E.g.:p: “If you turn in a homework late, then it

will not be graded”; “If you get 100% in this course, then you will get an A+”.

Conditional:p q [“if p then q”]

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p q p q

T T T

T F F

F T T

F F T

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Conditional statement

terminology

From the definition of a conditional statement find if this two statements are True or False and why???

“If today is Sunday ,then 2+6=8”

“If today is Sunday ,then 2+6=3”

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BiConditional:p q [“p iff q”]

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p q p q

T T T

T F F

F T F

F F T

Biconditional statement

terminology

• It is below freezing and it is snowing• It is below freezing but not snowing• It is not below freezing and it is not snowing• It is either snowing or below freezing (or

both)• If it is below freezing, it is also snowing• That it is below freezing is necessary and

sufficient for it to be snowing

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HW

Logical equivalent:

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((P)↔Q)≡(P↔(Q))

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