Question

If A be the set of all triangles and B the set of positive real numbers, then the mapping
f : A $\to$ B defined by
$f\left(\Delta \right)$ area of the triangle $\Delta ,\Delta \epsilon A$ is

• A. one-one onto
• B. one-one into
• C. many-one onto
• D. many one into

Answer 1

The correct option is C many-one onto

Since the area of any triangle is a positive real number,therefore f-image of any triangle
$\Delta \epsilon A$, i.e. $f\left(\Delta \right)\epsilon B$, corresponding to any real numbers in B, there is a triangle inA. Thus, f is onto.
Again there can be many triangles having the same area. Therefore, the mapping f is many-one
Hence, the mapping fis many-one onto