Question

Restate the following statements with appropriate conditions, so that they become true statements.

i.	For every real number x, $3x>x$.
ii.	For every real number x, $x^2\ge x$.
iii.	If you divide a number by two, you will always get half of that number.
iv.	The angle subtended by a chord of a circle at a point on the circle is ${90}^o$.
v.	If a quadrilateral has all its sides equal, then it is a square.

Answer 1

i.	If $x>0$, then $3x>x$.
ii.	If $x\le 0$ or $x\ge 1$, then $x^2\ge x$.
iii.	If you divide a number other than $0$ by $2$, then you will always get half of that number.
iv.	The angle subtended by a diameter of a circle at a point on the circle is ${90}^o$.
v.	If a quadrilateral has all its sides and interior angles equal, then it is a square.