Question

Which of the following are false?

$i.{\left(1\right)}^{2016}>{\left(1\right)}^{2014}$

$ii.{\left(1\right)}^{2016}>{\left(0\right)}^{2016}$

$iii.{\left(1\right)}^{2016}>{(-1)}^{2016}$

$iv.{(-1)}^{2014}>{(-1)}^{2015}$

• A. iii and iv
• B. i and iii
• C. i, iii, and iv
• D. i and ii

Answer 1

The correct option is B i and iii

As we know,

${\left(1\right)}^{anynumber}=1$

${(-1)}^{oddnumber}=-1$

${(-1)}^{evennumber}=+1$

${\left(0\right)}^{anynon-zeronumber}=0$

Now,
$i){\left(1\right)}^{2016}>{\left(1\right)}^{2014}⟹1>1,$
which is not possible, hence this statement is false.

$ii){\left(1\right)}^{2016}>{\left(0\right)}^{2016}⟹1>0,$
this statement is true.

$iii){\left(1\right)}^{2016}>{(-1)}^{2016}⟹1>1,$
which is not possible, hence this statement is false.

$iv){(-1)}^{2014}>{(-1)}^{2015}⟹1>(-1)$
this statement is true.

$\therefore$ Only i and iii are false.