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i've asked my dad what is the quotient map from MxM to (M/R)x(M/R)?

he told me it is qxq: MxM -> (M/R)x(M/R) defined by

(qxq)(x,y) = (q(x), q(y)),

but there are some conditions to be met, but he could not remember what those conditions are. i went through all 6 or so of my topology textbooks and could not find it.

does anybody know what the conditions are for qxq: MxM -> (M/R)x(M/R) defined by

(qxq)(x,y) = (q(x), q(y)),

to be a quotient map if q:M -> M/R is a quotient map???