Monogamy, mean having one partner/relationship at a time. Men and women as not restricted to only have a monogamous marriage. Polygamous relationships also exist in some part of the world. For example, in middle eastern societies.
Monogamy relationship/ marriage is one in which a person only have one partner for the lifetime/or at a time, unlike the opposite which is suggested in a polygamous relationship i.e. having multiple partners at a time.
As per the studies conduct in the recent past about ideal relationships, 61% agrees with monogamous relationship. And in Jan 2020 the percentage dropped to 56%. So the statement Worldwide men and women are only permitted to have monogamous marriages is false.
Therefore, the above given statement is false.
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