In a survey it was found that \(21\) people liked product \(A, 26\) liked product \(B\) and \(29\) liked product \(C\). If \(14\) people liked products \(A\) and \(B, 12\) people liked products \(C\) and \(A, 14\) people liked products \(B\) and \(C\) and \(8\) liked all the three products. Find how many liked product \(C\) only.

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In a survey it was found that \(21\) people liked product \(A, 26\) liked product \(B\) and \(29\) liked product \(C\). If \(14\) people liked products \(A\) and \(B, 12\) people liked products \(C\) and \(A, 14\) people liked products \(B\) and \(C\) and \(8\) liked all the three products. Find how many liked product \(C\) only.

\(11\)

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Let \(P, Q\), and \(R\) be the set of people who like product \(A\), product \(B\), and product \(C\) respectively.

\(n(P) = 21, n(Q) = 26, n(R) = 29, n(P \cap Q) = 14, n(R \cap P) = 12\),

\(n(Q \cap R) = 14, n(P \cap Q \cap R) = 8\)

The Venn diagram for the given problem can be drawn as

Number of people who like product \(C\) only is \({29 – (4 + 8 + 6)} = 11\)

\(n(P) = 21, n(Q) = 26, n(R) = 29, n(P \cap Q) = 14, n(R \cap P) = 12\),

\(n(Q \cap R) = 14, n(P \cap Q \cap R) = 8\)

The Venn diagram for the given problem can be drawn as

Number of people who like product \(C\) only is \({29 – (4 + 8 + 6)} = 11\)

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