Which of the following function f: Z X Z → Z is not onto?a.f(a, B) = a + bb.f(a, B) = ac.f(a, B) = a – bd.f(a, B) = |b|

The function that is not onto is d. f(a, B) = |b|.

Here's why:

An onto function (or surjective function) is a function where every element in the range is mapped to by at least one element in the domain. In other words, every possible output value is produced by at least one input value.

a. f(a, B) = a + b: This function is onto because for any integer z in Z, we can find a pair (a, b) such that a + b = z. For example, if z = 1, we can choose a = 1 and b = 0.

b. f(a, B) = a: This function is onto because for any integer z in Z, we can find a pair (a, b) such that a = z. For example, if z = 1, we can choose a = 1 and any value for b.

c. f(a, B) = a – b: This function is onto because for any integer z in Z, we can find a pair (a, b) such that a - b = z. For example, if z = 1, we can choose a = 2 and b = 1.

d. f(a, B) = |b|: This function is not onto because there is no way to produce a negative integer from the absolute value of an integer. The absolute value of an integer is always non-negative, so the negative integers in Z are not in the range of this function. Therefore, this function is not onto.