In the universal set of U = {English words}, here’s three sets: • A = {gem, rue, cat, roof} • B = {w | w is a 4-letter word} • C = {gem, rock, radio} List all the elements in the combination of sets below. Be sure to use proper set notation in your answers. (a) A ∩ B (b) A ∪ C (c) A ∩ C (d) Let W = {x | x is a 4-letter word from A or C}. Express W as a combination of A, B, and C using ∩, ∪ and complement.

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.