By definition
Rˉ={(a,b)∣(a,b)∈R}
This means that the set Rˉ consists of ALL POSSIBLE pairs {(x,y)∣x∈Aandy∈B} .
Since the set A consists of ∣A∣=n elements, and the set B consists of ∣B∣=m elements, then the number of possible pairs is
∣∣Rˉ∣∣=n⋅m
since the elements for the pair (x,y) are selected independently of each other.
ANSWER
∣∣Rˉ∣∣=mn
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