In this paper we are going to deal with some expressions in logic. These expressions have a constant meaning and they perform logical operations. These operations are;A-Conjunction performed by 'and'B-Disjunction performed by 'or'C-Implication performed by 'if…then'D-Equivalence performed by 'if and only if'E-negation performed by 'not'

These expressions are called 'logical connectives '

We are going to discuss 'propositional logic' the relations between simple sentences joined by any of

these connectors , to find out how the truth value of a complex proposition is determined by the truth values of its simple propositions and the connective joining

them . This can be illustrated as follows;Simple sentence + Simple sentence →↓→ Complex

sentence {proposition} ↓

Connective These relations go in the field of { propositional logic}*

2-There are many other connectives in natural languages such as 'but',;so', 'therefore','because',since',after

all',moreover','before','as','even though.'Linguists are less interested in natural connectives for two reasons.

1 )linguists are more interested in finding a perfect artificial language to master the rules of inference.

2 )These connectives do not carry a concept, thus cannot be translated into symbols of propositional logic

Ex. Tom is very handsome. After all he is rich, too .

From among the connectives in propositional logic, we are focused on three. The following are the connectives and how they are represented by .symbols

The relation the connective the symbolA .conjunction and

B. disjunction orC .implication if…then

These connectives are "truth functional", that is, they have constant meaning in logic.

Truth tableThe truth table of p AND q )also written as p q or p & q in ∧logic, p && q in many programming languages, or pq in electronics):

pqp&q

TTT

TFF

FTF

FFF

http://en.wikipedia.org/wiki/Grammatical_conjunction

Examples: )1) is true only if both )1a)And )1b) are true

)1 )Bill got up and went school )p &q))1a )Bill got up. )p)

)1b) Bill went to school )q)

)and )can have a variety of meanings.Consider these examples :

)1) )Ambiguity)Tom and peter own a car. )Do they have one car or each one has his own car )

)2 )Order of events )"and means" and then ") They got married and had a baby.

)3)and=conditional truth If they got married and a baby their parents would be pleased, put if they had a baby and got married , their parents would be upset

)4) and= causal relation .I dropped the camera and it broke

The implication is false only if the antecedent is true and the consequent is false .

In other cases it is true. See truth table

pq )p, q)

FFT

FTT

TFF

TTT

http://en.wikipedia.org/wiki/Logical_implicationImplication is expressed by "if", "if….then", "provided",

"whenever" or "unless" Implication is also known as a . " conditional"

*for example: *If it is raining ,then it will be wet.

*we rarely use implication in English, instead we use the strong corditional.

*If you mow the lawn ,I'll give you five dollas con ditionals are wed for a rariety of purposes such as epistemic conditionals and speech act

conditionals: )1 )If she is divorced, she s been married

)2 )John has left , if you haven't heard. )3 )they can also be used for stylistic reasons.

pq(p↔q)

TTT

TFF

FTF

FFT

Equivalence or biconditional is normally expressed by )If and only if – exactly when – only when –only if).

Example: Jane is at the party if and only if Matthew is at the party.

In English )if) can be difficult to distinguish from )if and only if) for example: the sentence )1) strongly suggest the if and only if interpretation. For example:

) 1 )I will help you if you are too busy to do it yourself.