Determine if the following statements are true or false. (a) if ∫c vector f · d vector r = 0 for one closed path c, then vector f is path-independent. true false (b) if the total change of a function f along a curve c is zero, then c must be a contour of f. true false (c) line integralc vector f · d vector r = vector f(q) - vector f(p) when p and q are the endpoints of c. true false (d) if vector f is continuous and vector f = gradf, then vector f is path-independent. true false (e) if f(x) and g(y) are continuous one-variable functions, then the vector field vector f = f(x)vector i + g(y)vector j is path-independent. true false (f) the vector field vector f( vector r ) = vector r in 3-space is path-independent.