# Twelve Statements End Determine Whether Universally True Given Finite Sets X Y Z Think Uni Q35261393  For each of the twelve statements in the end below, determine whether it is universally true for any given finite sets X, Y and Z. If you think it is not universally true for any given finite sets X, Y and Z. give a concrete counter does not hold. If you think it is universally true for any given finite sets X, Y and Z, write a direct proof to prove it. Note that to prove that AC B (set A is a subset of set B) is true using a direct proof, you need to show that ifr belongs to A (ie. I є A) then I also belongs to B (ie. I є B). To prove A = B using a direct proof, you need to prove both A C B and BCA. 1a) (X-Z)n(Y-Z) (Xn Y)-Z (3 points) b) (XnY)-Z(X-2)n(Y-Z) (3 points) d (xnY)-Z- (X -z)n(Y – z) (1 point 2a) (X – Z)U(Y – Z) S (XUY)- Z (3 points) b) (xU)-ZS(-Z)U(Y- Z) (3 points) c) (X U Y)-Z = (X-Z)U(Y-Z) (1 point) b) XN(Y-Z) c (xn Yn(X-Z) (3 points) c) XN(Y-Z) = (Xn Y)n(X-Z) (1 point) 4a (XUY)U(X- z)SXUY- Z) (3 points b) XU(Y-Z) S (XUYU(- Z) (3 points d XU(Y-Z) = (XU Y) U(X-Z) (1 point) Show transcribed image text

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