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Let [x] denote the greater integer $$\le x$$ and $$\left( x \right) $$ denote the lest integer $$\ge x.$$ Which of the following statements are True?

A
$$\left[ x \right] \left( y \right) =\left( x \right) \left[ y \right] $$ for all x,y
B
$$-\left[ x \right] =\left( -x \right) $$ for all x.
C
$$\left[ x \right] =\left( x \right) $$ if and only if $$x\epsilon Z$$
D
$$\left[ x \right] +1=\left( x \right) $$ id and only if $$x\epsilon Z$$
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Solution
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Correct option is A. $$\left[ x \right] =\left( x \right) $$ if and only if $$x\epsilon Z$$

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