Special Words Or Phrases




The connecting words which are found in compound statements like “And”, “Or”, etc. are often used in Mathematical Statements. These are called connectives. 

1)  The word “And”:
Let us look at a compound statement with “And”.
p: A point occupies a position and its location can be determined. 
The statement can be broken into two component statements as 
q : A point occupies a position.
r : Its location can be determined. 
Here, we observe that both statements are true.

2)  The word “Or”:
p: An ice cream or pepsi is available with a Thali in a restaurant.
This means that a person who does not want ice cream can have a pepsi along with Thali or one does not want pepsi can have an ice cream along with Thali. That is, who do not want a pepsi can have an ice cream. A person cannot have both ice cream and pepsi. This is called an exclusive “Or”.

Rule for the compound statement with ‘Or’:
For example, consider the following statement. 
p: Two lines intersect at a point or they are parallel 
The component statements are 
q: Two lines intersect at a point. 
r: Two lines are parallel. 
Then, when q is true r is false and when r is true q is false. 
Therefore, the compound statement p is true.

4)  Quantifiers :
Quantifiers are phrases like, “There exists” and “For all”. Another phrase which appears in mathematical statements is “there exists”. For example, consider the statement. p: There exists a rectangle whose all sides are equal. This means that there is atleast one rectangle whose all sides are equal. 
A word closely connected with “there exists” is “for every” (or for all). Consider a statement.

p: For every prime number p,`sqrt p` is an irrational number.

This means that if S denotes the set of all prime numbers, then for all the members p of the set S,`sqrt p` is an irrational number.

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