`\color{fuchsia}{★ul"Negation of a statement")`
`color(green)("The denial of a statement is called the negation of the statement.")`
If `p` is a statement, then the negation of `p` is also a statement and is `color(green)("denoted by ∼ p,")` and read as `"‘not p’."`
`color(red)("Let us consider the statement ")`:
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ color(blue)"p: New Delhi is a city"`
The negation of this statement is
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "It is not the case that New Delhi is a city"`
This can also be written as
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "It is false that New Delhi is a city."`
This can simply be expressed as
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ color(orange)"New Delhi is not a city."`
`\color{green} ✍️ \color{green} \mathbf(KEY \ CONCEPT) `
While forming the negation of a statement, phrases like, `"“It is not the case”"` or `"“It is false that”"` are also used.
Here is an example to illustrate how, by looking at the negation of a statement, we may improve our understanding of it.
`color(red)("Let us consider the statement")`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ color(orange)" p: Everyone in Germany speaks German."`
The denial of this sentence tells us that not everyone in Germany speaks German.
This does not mean that no person in Germany speaks German.
It says merely that `color(orange)"at least one person in Germany does not speak German."`
`\color{fuchsia}{★ul"Negation of a statement")`
`color(green)("The denial of a statement is called the negation of the statement.")`
If `p` is a statement, then the negation of `p` is also a statement and is `color(green)("denoted by ∼ p,")` and read as `"‘not p’."`
`color(red)("Let us consider the statement ")`:
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ color(blue)"p: New Delhi is a city"`
The negation of this statement is
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "It is not the case that New Delhi is a city"`
This can also be written as
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "It is false that New Delhi is a city."`
This can simply be expressed as
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ color(orange)"New Delhi is not a city."`
`\color{green} ✍️ \color{green} \mathbf(KEY \ CONCEPT) `
While forming the negation of a statement, phrases like, `"“It is not the case”"` or `"“It is false that”"` are also used.
Here is an example to illustrate how, by looking at the negation of a statement, we may improve our understanding of it.
`color(red)("Let us consider the statement")`
`\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ color(orange)" p: Everyone in Germany speaks German."`
The denial of this sentence tells us that not everyone in Germany speaks German.
This does not mean that no person in Germany speaks German.
It says merely that `color(orange)"at least one person in Germany does not speak German."`