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Let U = 1, 2, 3, , 60 be a universal set. Let P be the subset of U consisting of all multiples of 4 , and Q be the subset of U consisting of all multiples of 6 . The sum of all elements that belong to exactly one of the sets P or Q is

Correct answer

450

Step-by-step solution

Let U = 1, 2, 3, , 60 . The set P contains multiples of 4 up to 60 : P = 4, 8, 12, , 60 Number of terms in P , n(P) = 60 4 = 15 . Sum of elements in P = 15 2 (4 + 60) = 15 32 = 480 . The set Q contains multiples of 6 up to 60 : Q = 6, 12, 18, , 60 Number of terms in Q , n(Q) = 60 6 = 10 . Sum of elements in Q = 10 2 (6 + 60) = 5 66 = 330 . The intersection P Q contains multiples of LCM (4, 6) = 12 up to 60 : P Q = 12, 24, 36, 48, 60 Number of terms in P Q , n(P Q) = 60 12 = 5 . Sum of elements in P Q = 5 2 (12 + 60

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