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Question

If $$A= \{x:x^{2}-5x+6=0\}$$, $$B=\{2,4\}$$, $$C=\{4,5\}$$ then $$A\times(B\cap C)$$


A
{(2,4),(3,4)}
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B
{(4,2),(4,3)}
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C
{(2,4),(3,4),(4,4)}
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D
{(2,4),(3,4),(4,4),(5,5)}
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Solution

The correct option is A $$\{(2, 4), (3,4)\}$$
$$x^{2}-5x+6=0  \Rightarrow  (x-2)(x-3)=0  ; \ \  x=2,3$$

$$B\cap C=\left \{ 4 \right \}  ;  A=\left \{ 2,3 \right \}$$

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

$$=\left \{ (2,4),(3,4) \right \}$$

Mathematics

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