Question

Universal set, \[ U=\{x\mid x^5-6x^4+11x^3-6x^2=0\}; \quad A=\{x\mid x^2-5x+6=0\}; \quad B=\{x\mid x^2-3x+2=0\}. \] What is \((A\cap B)'\)?

• A. \(\{1,3\}\)
• B. \(\{1,2,3\}\)
• C. \(\{0,1,3\}\)
• D. \(\{0,1,2,3\}\)

Hint:

Complement is always taken with respect to universal set.

Answer 1

The Correct Option is C

Step 1: Solve: \[ U=\{0,1,2,3\},\quad A=\{2,3\},\quad B=\{1,2\} \]
Step 2: \[ A\cap B=\{2\} \]
Step 3: \[ (A\cap B)'=U-\{2\}=\{0,1,3\} \]