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Cartesian Product

If A = x ∈ N ...

Question

If A = {x $\in$ N : 3 $<$ x $\leq$ 6}, then find A $\times$ A.

A

{(4,5),(4,6),(5,4),(5,6),(6,4),(6,5)}

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B

{(4,4),(4,5),(4,6),(5,4),(5,5),(5,6),(6,4),(6,5),(6,6)}

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C

{(4,4),(4,5),(4,6),(5,5),(5,6),(6,6)}

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D

{(4,4),(4,5),(4,6),(5,4),(5,6),(6,4),(6,5)}

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Solution

The correct option is B {(4,4),(4,5),(4,6),(5,4),(5,5),(5,6),(6,4),(6,5),(6,6)}
Natural numbers which are greater than 3 and lless than equal to 6 are 4, 5, 6.
$∴$ A = {4,5,6}
A $\times$ A
$=$ {4,5,6} $\times$ {4,5,6}
$= (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)$

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