Set, Relations and FunctionsPYQ Dec 23Question 1908 of 217
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If A={1,2}\displaystyle A = \{1, 2\}, B={3,4}\displaystyle B = \{3, 4\}, C={5,6}\displaystyle C = \{5, 6\} then the value of A×(B∪C)\displaystyle A \times (B \cup C)

Options

A(1,2),(3,4),(5,6)\displaystyle (1,2), (3,4), (5,6)
B(1,3),(2,3),(1,4),(2,4),(2,5),(1,5),(1,6),(2,6)\displaystyle (1,3), (2,3), (1,4), (2,4), (2,5), (1,5), (1,6), (2,6)
C(1,3),(2,3),(1,4),(2,4),(2,5),(1,5),(3,1),(2,3),(4,1),(2,4),(2,5),(1,5),(1,6),(2,6)\displaystyle (1,3), (2,3), (1,4), (2,4), (2,5), (1,5), (3,1), (2,3), (4,1), (2,4), (2,5), (1,5), (1,6), (2,6)
D(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)\displaystyle (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6)
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Correct Answer

✅ Option d — (1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)\displaystyle (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6)

All Options:

  • A(1,2),(3,4),(5,6)\displaystyle (1,2), (3,4), (5,6)
  • B(1,3),(2,3),(1,4),(2,4),(2,5),(1,5),(1,6),(2,6)\displaystyle (1,3), (2,3), (1,4), (2,4), (2,5), (1,5), (1,6), (2,6)
  • C(1,3),(2,3),(1,4),(2,4),(2,5),(1,5),(3,1),(2,3),(4,1),(2,4),(2,5),(1,5),(1,6),(2,6)\displaystyle (1,3), (2,3), (1,4), (2,4), (2,5), (1,5), (3,1), (2,3), (4,1), (2,4), (2,5), (1,5), (1,6), (2,6)
  • D(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)\displaystyle (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6)

Detailed Solution & Explanation

Given sets:
A={1,2}\displaystyle A = \{1, 2\}
B={3,4}\displaystyle B = \{3, 4\}
C={5,6}\displaystyle C = \{5, 6\}
First, let us compute the union of B\displaystyle B and C\displaystyle C:
B∪C={3,4,5,6}B \cup C = \{3, 4, 5, 6\}
Now, we compute the Cartesian product A×(B∪C)\displaystyle A \times (B \cup C):
A×(B∪C)={1,2}×{3,4,5,6}A \times (B \cup C) = \{1, 2\} \times \{3, 4, 5, 6\}
The Cartesian product is the set of all ordered pairs where the first element is from A\displaystyle A and the second is from B∪C\displaystyle B \cup C:
A×(B∪C)={(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)}A \times (B \cup C) = \{(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6)\}
Hence, **Option D** is the correct answer.

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