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.