Relations and Functions — Important Questions

False

A × B ≠ B × A in general because ordered pairs care about position. (a,b) ≠ (b,a) unless a = b. They are equal only when A = B or one is empty.

True

A function requires: (1) every element of A must be mapped, (2) each element of A maps to exactly one element of B. This is the defining condition of a function.

5

|x| = −x when x < 0. So |−5| = −(−5) = 5. The modulus function always returns a non-negative value.

False

f(x) = x² ≥ 0 for all real x. So the range is [0, ∞), not all of R. Negative numbers like −1 are in the codomain but not in the range.