Q111 / 180 · COMEDK 2023 (Morning Shift) · Mathematics
If $A=\{a, b, c\}, B=\{b, c, d\}$ and $C=\{a, d, c\}$ then $(A-B) \times(B \cap C)$ is equal to
- Correct answerA$\{(a, c),(a, d)\}$
- B$\{(c, a),(d, a)\}$
- C$\{(a, c),(a, d),(b, d)\}$
- D$\{(a, b),(c, d)\}$
Solution
Given sets $A = \{a, b, c\}$, $B = \{b, c, d\}$, and $C = \{a, d, c\}$.
First, determine $A - B$. The set $A - B$ contains elements that are in $A$ but not in $B$.
$A - B = \{a, b, c\} - \{b, c, d\} = \{a\}$.
Next, determine $B \cap C$. The set $B \cap C$ contains elements common to both $B$ and $C$.
$B \cap C = \{b, c, d\} \cap \{a, d, c\} = \{c, d\}$.
Finally, compute the Cartesian product $(A - B) \times (B \cap C)$.
$(A - B) \times (B \cap C) = \{a\} \times \{c, d\} = \{(a, c), (a, d)\}$.
Answer: $\{(a, c),(a, d)\}$
First, determine $A - B$. The set $A - B$ contains elements that are in $A$ but not in $B$.
$A - B = \{a, b, c\} - \{b, c, d\} = \{a\}$.
Next, determine $B \cap C$. The set $B \cap C$ contains elements common to both $B$ and $C$.
$B \cap C = \{b, c, d\} \cap \{a, d, c\} = \{c, d\}$.
Finally, compute the Cartesian product $(A - B) \times (B \cap C)$.
$(A - B) \times (B \cap C) = \{a\} \times \{c, d\} = \{(a, c), (a, d)\}$.
Answer: $\{(a, c),(a, d)\}$
Hence, the correct answer is option: 'A'.