Explanation:
C Given, \(U=\left\{x \mid x^5-6 x^4+11 x^3-6 x^2=0\right\}\)
\(\mathrm{A}=\left\{\mathrm{x} \mid \mathrm{x}^2-5 \mathrm{x}+6=0\right\}\)
\(\mathrm{B}=\left\{\mathrm{x} \mid \mathrm{x}^2-3 \mathrm{x}+2=0\right\}\)
Solve U,
\(U(0)=0\)
\(U(1)=0\)
\(U(2)=0\)
\(U(3)=0\)
Then, \(\mathrm{U}=\{0,1,2,3\}\)
Solve A,
\(A=\{2,3\}\)
\(A(2)=0\)
\(A(3)=0\)
Solve B,
\(B(1)=0\)
\(B(2)=0\)
Then, \(B=\{1,2\}\)
From solving U, A and B we get -
\(\mathrm{U}=\{0,1,2,3\}\)
\(\mathrm{A}=\{2,3\}\)
\(\mathrm{B}=\{1,2\}\)
Then, \(A \cap B=\{2,3\} \cap\{1,2\}\)
\(A \cap B=\{2\}\)
So,
\((\mathrm{A} \cap \mathrm{B})^{\prime} =\mathrm{U}-(\mathrm{A} \cap \mathrm{B})\)
\(=\{0,1,2,3\}-\{2\}\)
\((\mathrm{A} \cap \mathrm{B})^{\prime} =\{0,1,3\}\)