Let $A = \{ x \in R:[x + 3] + [x + 4] \le 3\} ,$ $B = \left\{ {x \in R:{3^x}{{\left( {\sum\limits_{r = 1}^\infty {{3 \over {{{10}^r}}}} } \right)}^{x - 3}} < {3^{ - 3x}}} \right\},$ where [t] denotes greatest integer function. Then,

Question

Let $A = \{ x \in R:[x + 3] + [x + 4] \le 3\} ,$

$B = \left\{ {x \in R:{3^x}{{\left( {\sum\limits_{r = 1}^\infty {{3 \over {{{10}^r}}}} } \right)}^{x - 3}} < {3^{ - 3x}}} \right\},$ where [t] denotes greatest integer function. Then,

$B \subset C,A \ne B$

$A \subset B,A \ne B$

$A = B$

$A \cap B = \phi $

Solution

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