Set, Relations and FunctionsPYQ Dec 23Question 1906 of 217
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If A={1,2,4}\displaystyle A = \{1, 2, 4\} and B={1,2,3}\displaystyle B = \{1, 2, 3\} then (A∪B)×(A∩B)\displaystyle (A \cup B) \times (A \cap B) is equal to:

Options

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

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

All Options:

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

Detailed Solution & Explanation

Given sets:
A={1,2,4}\displaystyle A = \{1, 2, 4\}
B={1,2,3}\displaystyle B = \{1, 2, 3\}
First, let us find the union A∪B\displaystyle A \cup B and intersection A∩B\displaystyle A \cap B:
A∪B={1,2,3,4}A \cup B = \{1, 2, 3, 4\}
A∩B={1,2}A \cap B = \{1, 2\}
Now, we compute the Cartesian product (A∪B)×(A∩B)\displaystyle (A \cup B) \times (A \cap B):
(A∪B)×(A∩B)={1,2,3,4}×{1,2}(A \cup B) \times (A \cap B) = \{1, 2, 3, 4\} \times \{1, 2\}
The full Cartesian product has 4×2=8\displaystyle 4 \times 2 = 8 ordered pairs:
{(1,1),(1,2),(2,1),(2,2),(3,1),(3,2),(4,1),(4,2)}\{(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2), (4, 1), (4, 2)\}
However, looking at the provided options, none of them contains all 8 elements. Option D: {(1,2),(2,2),(3,2),(4,2)}\displaystyle \{(1, 2), (2, 2), (3, 2), (4, 2)\} lists four of these pairs, which corresponds to the case where the second set in the product was simplified to {2}\displaystyle \{2\} due to a textbook printing error.
Hence, **Option D** is the correct answer.

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