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Compute (A-B)×(B∩C) for Three Given Sets | JEE Sets

JEE Maths question with a full step-by-step solution.

Question
If A={a,b,c}A = \{a, b, c\}, B={b,c,d}B = \{b, c, d\} and C={a,d,c}C = \{a, d, c\}, then (A−B)×(B∩C)(A - B) \times (B \cap C) is equal to
A{(a,c),(a,d)}\{(a, c), (a, d)\}correct
B{(a,b),(c,d)}\{(a, b), (c, d)\}
C{(c,a),(a,d)}\{(c, a), (a, d)\}
D{(a,d),(a,d),(b,d)}\{(a, d), (a, d), (b, d)\}
Solution
Step 1: A−BA - B keeps elements of AA not in BB:
A−B={a}.A - B = \{a\}.
 Step 2: B∩CB \cap C keeps elements common to BB and CC:
B∩C={c,d}.B \cap C = \{c, d\}.
 Step 3: Take the Cartesian product:
(A−B)×(B∩C)={a}×{c,d}={(a,c),(a,d)}.(A - B) \times (B \cap C) = \{a\} \times \{c, d\} = \{(a, c), (a, d)\}.
 Correct answer: (1)
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