A) 2
B) 3
C) 4
D) 5
Correct Answer: B
Solution :
we have, \[\operatorname{U}=\left\{ x:{{x}^{5}}-6{{x}^{4}}+11{{x}^{3}}-6{{x}^{2}}=0 \right\}\]\[=\{0,1,2,3\}\] |
\[\operatorname{A}=\left\{ x:{{x}^{2}}-5x+6=0 \right\}=\left\{ 2,3 \right\}\] |
and \[\operatorname{B}=\left\{ x:{{x}^{2}}-3x+2=0 \right\}=\left\{ 1,2 \right\}\]\[\therefore \operatorname{A}\cap B=\{2\}\] |
Hence, \[\left( \operatorname{A}\cap \operatorname{B} \right)=\operatorname{U}-\left( \operatorname{A}\cap \operatorname{B} \right)\] |
\[=\left\{ 0,1,2,3 \right\}-\left\{ 2 \right\}\] |
\[=\left\{ 0,1,3 \right\}\] |
\[\therefore n\left( A\cap B \right)'=3\] |
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