Problem $1(6$ pt$)$ DISCRETE MATHS$)$ PLEASE WRITE THE CORRECT ANSWERS:

From the list below choose the relation $f$ that is a function and identify its domain and range.

$($a$)f$ assigns to a bit string of length $10$ a position of $0-$bit in it$.$

$($b$)f$ assigns to a bit string of the length not exceeding $10$ a number of $0-$bits in it$.$

$($c$)f$ assigns to an $n$ another integer $m$ using equation $n=+-m.$

$($d$)f$ assigns to a real number $x$ a real number $y$ using equation $y^2=x.$