Let X be a set. If A X is a subset of X the characteristic function of A is the function x- (0,11 given by xA(ar) 0 if z E A A. R if 1 Let A and B be two subsets of X. Prove that (a) XAnB XAXB

Is there a direction u in which the rate of change of f(x, y)equals=x squared minus 3 xy plus 4 y squaredx2−3xy+4y2 at p(1,2) equals 14? give reasons for your answer. choose the correct answer below. a. no. the given rate of change is smaller than the minimum rate of change. b. no. the given rate of change is larger than the maximum rate of change. c. yes. the given rate of change is larger than the minimum rate of change and smaller than the maximum rate of change.