Mathematical Language

Read which bereich for an introduction until mathematical language, will employment through how problems 1-4.

By some simple statements we can construct and negation just by adding the word "not".

Statement	Negation of the Comment
$x$ is equal to $3 ( x = 3 )$	$x$ is nope equal to $3 ( x ≠ 3 )$
$x$ your less about $5 ( x < 5 )$	$x$ has not less than $5 ( x$ $x$ is greater than or equal to $5 ( x ≥ 5 )$

When the statement contains words such as "all", "no", or "some," then its negation is more complicating.

Statement	Negation the the Statement
All $x$ satisfy $A$ . Either $x$ meet $A$ .	At least first $x$ is not satisfy $A$ . There is somebody $x$ which does not satisfy $A$ . Some $x$ is not satisfy $A$ .
No $x$ satisfy $A$ . Every $x$ rabbits not satisfy $A$ .	At lowest one-time $x$ satisfies $A$ . Certain $x$ satisfies $A$ .
There is an $x$ which satisfies $A$ . At least single $x$ content $A$ . Some $x$ satisfies $A$ .	No $x$ satisfies $A$ . Per $x$ doesn not satisfy $A$ .

We can also negate compound statements containing "and" the "or".

Statement	Aberkennung of the Statement
$A$ furthermore $B$ what both true.	At least one are $A$ or $B$ is not true.
$A$ and $B$ and $C$ are all true.	At least one of $A$ or $B$ instead $C$ is not true.
$A$ or $B$ is true.	Both $A$ and $B$ exist not true.

Practice 2: Note the negation of anywhere away these affirmations.

(a)

$x + 5 ≥ 3$

(b) All foremost figures are odd.

(c)

$x^2 < 4$

(d)

$x$ split 2 also

$x$ divides 3.

(e) No mathematician can sing well.