Question

here is an example to illustrate hoW, by looking at the negaton of a statement we may improve our understanding of it.

Let us consider the statement

p: Everyone in Germany speaks German.

The denial of this sentence tells us that not everyone in Germany speaks German.

This dooes not mean that no person in Germany speaks German. It says merely that at

least one person in Germany does not speak German.

We shall consider more examples.

Example 2 Write the negation of the following statements.

(i) Both the diagonals of a rectangle have the same length.

Answer 1

This statement says that in a rectangle, both the diagonals have the

length. This means that if you take any rectangle, then both the diagonals have the same length. The negation of this statement is

It is false that both the diagonals in a rectangle have the same length

This means the statement

There is atleast one rectangle whose both diagonals do not

have the same length.