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Answer :

With Y = {b, r, e, a, t, h} and Z = {l, a, u, g, h, t, e, r}, their union is

Y U Z = {b, r, e, a, t, h, l, u, g}

Then with X = {n, u, m, b, e, r}, the intersection with Y U Z is

X ∩ (Y U Z) = {u, b, e, r}