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Question Number 125645 by aurpeyz last updated on 12/Dec/20

In a certain set of 200 students.   subset A are blondes and the rest are  brunettes. B are left handed. and   C are left−handed blondes.    (1)Express in terms of A B C the   subset consisting of right−handed  brunettes.  (a) A ∪B ∩C (b)A^1 ∩B^1  (c)(A∪B)  (d) A∪B−C    (2) if A contains 80 students  B contains 24 and C contains 10.   how many right handed brunettes  are there?

$${In}\:{a}\:{certain}\:{set}\:{of}\:\mathrm{200}\:{students}.\: \\ $$$${subset}\:{A}\:{are}\:{blondes}\:{and}\:{the}\:{rest}\:{are} \\ $$$${brunettes}.\:{B}\:{are}\:{left}\:{handed}.\:{and}\: \\ $$$${C}\:{are}\:{left}−{handed}\:{blondes}. \\ $$$$ \\ $$$$\left(\mathrm{1}\right){Express}\:{in}\:{terms}\:{of}\:{A}\:{B}\:{C}\:{the}\: \\ $$$${subset}\:{consisting}\:{of}\:{right}−{handed} \\ $$$${brunettes}. \\ $$$$\left({a}\right)\:{A}\:\cup{B}\:\cap{C}\:\left({b}\right){A}^{\mathrm{1}} \cap{B}^{\mathrm{1}} \:\left({c}\right)\left({A}\cup{B}\right) \\ $$$$\left({d}\right)\:{A}\cup{B}−{C} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:{if}\:{A}\:{contains}\:\mathrm{80}\:{students} \\ $$$${B}\:{contains}\:\mathrm{24}\:{and}\:{C}\:{contains}\:\mathrm{10}.\: \\ $$$${how}\:{many}\:{right}\:{handed}\:{brunettes} \\ $$$${are}\:{there}? \\ $$

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