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Set Theoryhard
0:00.0

Consider a universal set U={1,2,…,20}U = \{1, 2, \dots, 20\}U={1,2,…,20}. Let A={x∈U∣xextisamultipleof3}A = \{x \in U \mid x ext{ is a multiple of } 3\}A={x∈U∣xextisamultipleof3}, B={x∈U∣xextisamultipleof5}B = \{x \in U \mid x ext{ is a multiple of } 5\}B={x∈U∣xextisamultipleof5}, and C={x∈U∣xextisaprimenumber}C = \{x \in U \mid x ext{ is a prime number}\}C={x∈U∣xextisaprimenumber}. Determine the cardinality of the set (A∩B)∖C(A \cap B) \setminus C(A∩B)∖C.