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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

If A = \ x: x^ 2 - 5x + 6 = 0\ , B = \ 2, 4\ , C = \ 4, 5\ , then A...

If A={x:x2−5x+6=0},B={2,4},C={4,5},A = \left\{x: x^{2} - 5x + 6 = 0\right\}, B = \left\{2, 4\right\}, C = \left\{4, 5\right\}, then A×(B∩C)isA \times \left(B \cap C\right) is

Options

  1. A{(2,4),(3,4)}\left\{\left(2, 4\right), \left(3, 4\right)\right\}
  2. B{(4,2),(4,3)}\left\{\left(4, 2\right), \left(4, 3\right)\right\}
  3. C{(2,4),(3,4),(4,4)}\left\{\left(2, 4\right), \left(3, 4\right), \left(4, 4\right)\right\}
  4. D{(2,2),(3,3),(4,4),(5,5)}\left\{\left(2, 2\right), \left(3, 3\right), \left(4, 4\right), \left(5, 5\right)\right\}

Correct answer

A. {(2,4),(3,4)}\left\{\left(2, 4\right), \left(3, 4\right)\right\}

Step-by-step solution

Clearly, A=A =\left\{2, 3\right\}, B = {2,4},C={4,5}\left\{2, 4\right\}, C = \left\{4, 5\right\}

B∩C={4}B \cap C = \left\{4\right\}

∴A×(B∩C)={(2,4),(3,4)}∴A \times \left(B \cap C\right) = \left\{\left(2, 4\right),\left(3, 4\right)\right\}
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