Question

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

• A. $\{1,3\}$
• B. $\{1,2,3\}$
• C. $\{0,1,3\}$
• D. $\{0,1,2,3\}$
• E. None of these

Hint:

To find $A \cap B$, list elements of both sets and select only the common elements.

Answer 1

Answer: (E)

Step 1: Find the elements of set $A$. \[ x^2 - 5x + 6 = 0 \Rightarrow (x-2)(x-3)=0 \] \[ A = \{2,3\} \]
Step 2: Find the elements of set $B$. \[ x^2 - 3x + 2 = 0 \Rightarrow (x-1)(x-2)=0 \] \[ B = \{1,2\} \]
Step 3: Find the intersection of $A$ and $B$. \[ A \cap B = \{2\} \]
Step 4: Compare with the given options. The correct intersection $\{2\}$ is not present in any of the options.