Is it contrary to Qur'an if a woman becomes a president?

I can't find any specific verse in the Quran that says a woman cannot be President (I may be wrong). But I found several verses that will make it difficult, if not impossible for a woman to be President;

Women have rights that are similar to men, but men are "a degree above them." 2:228

A woman is worth one-half a man. 2:282

Men are in charge of women, because Allah made men to be better than women. Refuse to have sex with women from whom you fear rebellion, and scourge them. 4:34

Women are feeble and are unable to devise a plan. 4:98

Believing women must lower their gaze and be modest, cover themselves with veils, and not reveal themselves except to their husbands, relatives, children, and slaves. 24:31

Women must cover themselves when in public. 33:59

First answer by Itchie.c2. Last edit by Itchie.c2. Contributor trust: 614 [recommend contributor]. Question popularity: 22 [recommend question]