Topic:- DISCRETE MATHEMATICSName : Seerat AbbasRoll No : 13Superior University Lahore(Multan campus)

ObjectiveIntroduction of Discrete MathPropositionCompound PropositionConjunctionDisjunctionNegationConditional StatementBi-ConditionalTruth Tables

`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:

1. The number of students in a class (and it is opposite to continous data)

Application It is a wide range subject its

study includes parts of logic , computer science ,statistics,and operations research,algebra,graphs etc.

Propositions “A declrative stetement that is

either True or False but not Both ”

• Represented by lowercase letters such as

p, q and r.

Examples of Proposition1. Islamabad is the Capital of

Pakistan2. Karachi is the Capital of Pakistan3. 2+2=44. 2+5=6This is not the Example of

Proposition:1.x+1=2 2.x+y=z3.What time is it 3.Read this

Carefully

F

FT

T

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".

Connectives “Used to combine propositions”

Some kinds of Connectives:1. Conjuction

2.Disjunction3. Conditional 4.Bi-conditional5. Negation

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:

qp

(Read as “p and q”) qp

qp

Truth table of Conjuction

P Q

T T TT F FF T FF F F

qp

An other Example of Conjuction

p: Today is Monday.q: it is raining.

Today is Monday AND it is raining.

qp

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”)

qp

qp qp

Truth table of Disjunction

P Q

T T TT F TF T TF F F

qp

DISJUNCTION

p: Today is Monday.q: it is raining.

Today is Monday OR it is raining.

qp

NEGATION“Let p be the proposition then the negation of p is denoted by and is the opposite proposition of p ”

Symbolically

p p

p

(Read as “not p”)

PT FF T

p

Truth tablep

NEGATION

p: Today is Monday.q: it is raining.

-p: Today is NOT Monday.-q: It is NOT raining.

p

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 false;otherwise true.

P QT T TT F TF T TF F F

p q

CONDITIONAL STATEMENT

p: Today is Monday.q: it is raining.

p qIF today is Monday, THEN it is

raining.

Bi-CONDITIONAL STATEMENT “Another comman statement is of the

form “p if and only if q”. Such statement are called Bi-conditional stetement”

Symbolicallyp q

(Read as “p if and only if q”)Condition:The condition p q is true when both p and q have same truth values;otherwise false

P QT T TT F FF T FF F T

p q

BICONDITIONAL STATEMENT

p: Today is Monday.q: it is raining.

Today is Monday IF AND ONLY IF it is raining.

qp