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Let  and relation  on  be  R . How many relations S on A satisfy ?

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Let A equals not stretchy left curly bracket 1 comma 2 comma 3 comma 4 not stretchy right curly bracket and relation R on A be Rblank equals not stretchy left curly bracket not stretchy left parenthesis a comma b not stretchy right parenthesis text end text straight ∣ text end text a minus b text  is divisible by 2 end text not stretchy right curly bracket. How many relations S on AA satisfy R subset of or equal to S subset of or equal to A cross times A?
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