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Solving a Set Equation: P ∪ Q and Exclusive Elements

This article delves into the mathematical problem of finding the values of sets P and Q based on the equation P ∪ Q = 20. We dissect the equation 8x + 4 = 20, leading to the determination of x. With x calculated as 2, we explore the implications for sets P and Q, determining P Q and their intersections. The overall goal is to systematically solve related set problems and clarify the concepts of union, intersection, and set differences in a concise mathematical framework.

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Solving a Set Equation: P ∪ Q and Exclusive Elements

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  1. #Q = #U=20 Higher paper 2 Q2 C (ii): Sets #(PnQ)=x 2x + x + 5x + 4 = 20 8x+4=20 8x = 16 x = 2 #(Q) = 12 #(P\Q)=2x #((PuQ)’)=4 U(20) (3x) (6x) P Q 2x x 5x 4

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