Discrete Mthematics by Seerat Abbas

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Topic- DISCRETE MATHEMATICS
Name Seerat Abbas Roll No 13 Superior
University Lahore(Multan campus)
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Objective

• Introduction of Discrete Math
• Proposition
• Compound Proposition
• Conjunction
• Disjunction
• Negation
• Conditional Statement
• Bi-Conditional
• Truth Tables

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Discrete Math

• Discrete mathematics is the
  mathematical structure that are fundamentally
  discrete rather than continious
• (In general it is used whenever objects are
  counted and when relationship between two
  finite(or countable) sets are studied.) For
  example
• The number of students in a class (and it is
  opposite to continous data)

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Application
It is a wide range subject its study
includes parts of logic , computer science
,statistics,and operations research,algebra,graphs
etc.
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Propositions

• A declrative stetement that is either
  True or False but not Both
• Represented by lowercase letters such as
• p, q and r.

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Examples of Proposition
T

• Islamabad is the Capital of Pakistan
• Karachi is the Capital of Pakistan
• 224
• 256
• This is not the Example of Proposition
• 1.x12 2.xyz
• 3.What time is it 3.Read this Carefully

F
T
F
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COMPOUND STATEMENT
Many mathematical statements are constructed by
combining one or more propositional, new
propositional is called compound proposition For
example, "Today is Monday and It is Raining" is
considered a compound statement.  The two simple
statements " Today is Monday " and " It is
Raining " are connected by the word "and".
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Connectives

• Used to combine propositions
• Some kinds of Connectives
• Conjuction
  2.Disjunction
• 3. Conditional 4.Bi-conditional
• 5. Negation

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CONJUCTION

• Any two Proposition can be combined by the word
  and to form a compound proposition called
  conjuction
• Symbolically
• Definition If p and q are true, then
  is true othervise is false

(Read as p and q)
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Truth table of Conjuction
P Q
T T T
T F F
F T F
F F F
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An other Example of Conjuction

• p Today is Monday.
• q it is raining.
• Today is Monday AND it is raining.

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DISJUNCTION

• Any two Proposition can be combined by the word
  or to form a compound proposition called
  disjuction
• Symbolically
• Definition If p and q are false, then
  is false othervise is
  true

(Read as p or q)
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Truth table of Disjunction
P Q
T T T
T F T
F T T
F F F
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DISJUNCTION

• p Today is Monday.
• q it is raining.
• Today is Monday OR it is raining.

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NEGATION

• Let p be the proposition then the negation of p
  is denoted by and is
  the opposite proposition of p
• Symbolically

Truth table
P
T F
F T
(Read as not p)
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NEGATION

• p Today is Monday.
• q it is raining.
• -p Today is NOT Monday.
• -q It is NOT raining.

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CONDITIONAL STATEMENT

• Many stetements, particularly in mathematics,
  are of the form if p then q. Such statement are
  called conditional stetement
• Symbolically
• p q
• (Read as p implies q)
• Condition
• The condition p q is
• false when p is true and
• q is falseotherwise true.

p q
P Q
T T T
T F T
F T T
F F F
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CONDITIONAL STATEMENT

• p Today is Monday.
• q it is raining.
• p q
• IF today is Monday, THEN it is raining.

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Bi-CONDITIONAL STATEMENT
Another comman statement is of the form p if
and only if q. Such statement are called
Bi-conditional stetement Symbolically p
q (Read as p if and only if q) Condition The
condition p q is true when both p and q
have same truth valuesotherwise
false
p q
P Q
T T T
T F F
F T F
F F T
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BICONDITIONAL STATEMENT
p Today is Monday. q it is raining. Today
is Monday IF AND ONLY IF it is raining.
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