Please show me the process. Thank you !!! Suppose A is a set. If F and G are par

Question

Please show me the process.  Thank you !!!

Suppose A is a set. If F and G are partitions of A. then we'll say that F refines G if X F Y G(X Y). Let P be the set of all partitions of A, and let R = {(F, G) P times P F refines G}. Prove that R is a partial order on P. Suppose that S and T are equivalence relations on A. Let F = A/S and G = A/T. Prove that S T iff F refines G. Suppose F and G are partitions of A. Prove that F G is the greatest lower bound of the set {F, G} in the partial order R. See exercise 17 for the meaning of the notation used here.)

Explanation / Answer

15) fx = -sin(x+2y+3z) * 1

fxy = -cos(x+2y+3z) * 2 = -2cos(x+2y+3z)

fxyz = -2* -sin(x+2y+3z) * 3 = 6 sin(x+2y+3z)

fy = -sin(x+2y+3z) *2

fyz = -2* cos(x+2y+3z) * 3 = -6*cos(x+2y+3z)

fyzx = -6* -sin(x+2y+3z) *1 = 6*sin(x+2y+3z)

fz = -sin(x+2y+3z) *3

fzx = -3* cos(x+2y+3z) *1 = -3*cos(x+2y+3z)

fzxy = -3* -sin(x+2y+3z) *2 = 6*sin(x+2y+3z)

fxyz = fyzx = fzxy = 6*sin(x+2y+3z)

fxyz = fyzx = fzxy

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