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Sets, Relations and Functions

In an examination, $34 %$ of the candidates fail in Arithmetic and $42 %$ in English. If $20 %$ fail in Arithmetic and English, the percentage of those passing in both subjects is :

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Sets, Relations and Functions

In an examination $80 %$ passed in English, $85 %$ in Maths, $75 %$ in both and $40$ students failed in both subjects. Then the number of students appeared are

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Sets, Relations and Functions

If $n (ξ) = 32, n (A) = 20, n (B) = 16$ and $n ((A \cup B)^{'}) = 4,$ find : $n (A \cup B)$

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Sets, Relations and Functions

If $n (A - B) = 12, n (B - A) = 16$ and $n (A \cap B) = 5,$ find: (i) $n (A)$ (ii) $n (B)$ (iii) $n (A \cup B)$

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Sets, Relations and Functions

In a class, $20$ opted for Physics, $17$ for Maths, $5$ for both and $10$ for other subjects. The class contains how many students?

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Sets, Relations and Functions

P, Q and R are three sets and $ξ = P \cup Q \cup R$ . Given that $n (ξ) = 60, n (P \cap Q) = 5, n (Q \cap R) = 10, n (P) = 20$ and $n (Q) = 23$ , find $n (P \cup R)$

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Sets, Relations and Functions

In the Venn diagram, the numbers represent the number of elements in the subsets. Given that $ξ = F \cup G \cup H$ and $n (ξ) = 42$ , find $n (G^{'} \cup H)$