Mathematics STATEMENT:

STATEMENT:

A sentence is called a mathematically acceptable statement if it is either true or false but not both.
A statement is neither imperative, nor interrogative nor exclamatory. A sentence which is a request, or a command is not a statement.
`Ex:` The following are the statements
`\ \ \ \ \ \ \ \ (a)` `6` is less than `8`
`\ \ \ \ \ \ \ \(b)` `2` is an odd number
`\ \ \ \ \ \ \ \(c)` Every square is a rectangle
`\ \ \ \ \ \ \ \(d)` New Delhi is in India
`text(Note :)` A sentence which is both true and false simultaneously is not a statement. Such a sentence is called a `text(paradox.)`

`text(Open Statement :)`
A declarative sentence containing variable `(s)` is an open statement if it becomes a statement when the variable`(s)` is (are) replaced by some definite value `(s)`.
`e.g.` `s = x` is an integer
`\ \ \ \ s` is true if `x` is integer and false if `x` is not integer.

`text(Compound Statements :)`
A compound statement is a statement which is made up of two or more statements. In this case, each statement is called a component statement.
`e.g.` All rational numbers are real and all real numbers are complex.
The component statement are
`\ \ \ \ \ \ \ p :` all rational numbers are real
`\ \ \ \ \ \ \ \ q :` all real numbers are complex numbers

 
SiteLock