Answer
Coming from a woman, no. Gender has nothing to do with it. It's all about the individual.
It depends, men tend to think that they are more logical because they don't include anger or aggression as an emotional response and try to limit the definition of "emotion" to activities like crying.
Emotional men who act out of anger or aggression are likely far less logical than women who do not.
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No, women are not less intelligent than men are. But they aren't more intelligent than men, either. Studies have shown that with some men and women, men tend to excel in some areas, while women tend to excel in others. But in general, they are the same intelligence.
And, while one sex may be more educated than the other, that's not the same as intelligence. So the level of education cannot be considered as a factor when measuring intelligence.