Q51 / 125 · BITSAT 2015 · Mathematics

Universal set, $U=\left\{x \mid x^{5}-6 x^{4}+11 x^{3}-6 x^{2}=0\right\}$ $A=\left\{x \mid x^{2}-5 x+6=0\right\}$ $\mathrm{B}=\left\{\mathrm{x} \mid \mathrm{x}^{2}-3\mathrm{x}+2=0\right\}$ What is $(A \cap B)^{\prime}$ equal to ?

  • A
    {1,3}
  • B
    {1,2,3}
  • Correct answer
    C
    {0,1,3}
  • D
    {0,1,2,3}

Solution

$U=\left\{x: x^{5}-6 x^{4}+11 x^{3}-6 x^{2}=0\right\}$ Solving for values of $x$, we get $\mathrm{U}=\{0,1,2,3\}$ $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}^{2}-5 \mathrm{x}+6=0\right\}$ Solving for values of $x$, we get $\mathrm{A}=\{2,3\}$ and $\mathrm{B}=\left\{\mathrm{x}: \mathrm{x}^{2}-3 \mathrm{x}+2=0\right\}$ Solving for values of $x$, we get $\mathrm{B}=\{2,1\}$ $A \cap B=\{2\}$ $\therefore(A \cap B)^{\prime}=U-(A \cap B)$ $=\{0,1,2,3\}-\{2\}=\{0,1,3\}$

Hence, the correct answer is option: 'C'.

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