The statement is given by:
∀ x , [tex]x^4>x[/tex]
This statement is false
Since, if we consider,
[tex]x=\dfrac{1}{2}[/tex]
then we have:
[tex]x^4=(\dfrac{1}{2})^4\\\\i.e.\\\\x^4=\dfrac{1}{2^4}\\\\i.e.\\\\x^4=\dfrac{1}{16}[/tex]
Also, we know that:
[tex]\dfrac{1}{16}<\dfrac{1}{2}[/tex]
( Since, two number with same numerator; the number with greater denominator is smaller than the number with the smaller denominator )
Hence, we get:
[tex]x^4<x[/tex]
when [tex]x=\dfrac{1}{2}[/tex]
Hence, the result :
[tex]x^4>x[/tex] is not true for all x belonging to real numbers.
Hence, the given statement is a FALSE statement.
