In mathematics we use sentences that can be shown to be either true or false but not both. Such sentences are called Statements. Thus,
A statement is a sentence which is either true or false but not both.
Example 1: Suns rises in the east.
This is a statement which is true.
Example 2: 4+4=5
This is a statement which is false.
Example 3: The garden is very beautiful.This is only a sentence not a statement because we need further information to decide whether the sentence is true or false. We need information like "What is the name of the garden and where it is located?".
Connectives
Many Statements are the combination of simple statements with some connecting words. These words are called connectives. The statements that are composed of other simple statements with the connectives are called Compound Statements.
Observe the following examples.
Example1: p: All primes but two are odd.
q: 2 is an even prime.
We can form a number of compound statements composed of these two. A few are listed below.
(i) All primes but 2 are odd and 2 is an even prime.
i.e., p and q.
(ii) All primes but 2 are odd or 2 is an even prime.
i.e., p or q.
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