First: If the shoes are removed after wiping over them, it is necessary to wipe over the socks; because wiping over the shoes is not the same as wiping over the socks. Unlike wiping over a two-part shoe, which connects two layers of leather, where one acts as the upper and the other as the lining, if one part is removed, there is no need to repeat the wiping over what is underneath; because the two parts are considered as one entity. Wiping over one part is like wiping over both, so if one is removed, it does not affect the validity of the wiping. However, the shoes and the socks are two distinct and separate items, and wiping over one does not count as wiping over the other. Therefore, if the shoes are removed, the socks remain without purification, and it is necessary to repeat the wiping over them. Second: If one of the shoes is removed, the wiping over both is invalidated, and the wiping over the remaining shoe and sock must be repeated; because the purification of the feet is indivisible, as they are considered one function. Thus, it is not permissible to wash one and wipe over the other. If one is invalidated, the other is also invalidated due to the necessity of indivisibility. Third: If one puts their hand under the shoes and wipes over the socks, this is not permissible due to the obligation to wipe over the shoes. Fourth: If the shoes are made of leather or similar material that allows walking on them, it is permissible to wipe over them, whether they are worn separately or over the socks. Fifth: If the shoe is made of cotton or similar material, wearing them separately does not allow for wiping over them; because they cannot support walking. However, if they are worn over the socks, wiping over them is only permissible if the moisture from the wiping does not reach the inner sock, in which case wiping is allowed to achieve the intended purpose. Sixth: If one wears a shoe over a thin sock, it is permissible to wipe over the shoe; because the connection of the worn item, whether shoe or otherwise, to the foot is not a condition; if it were a condition, wiping over the shoes would not be permissible. Seventh: If one wears the shoe over a thin sock, it is permissible to wipe over the shoe; because the connection of the worn item, whether shoe or otherwise, to the foot is not a condition; if it were a condition, wiping over the shoe would not be permissible. See: "Umda al-Ri'aya" 1: 111, "Al-Tabyin" 1: 52, "Sharh al-Wiqaya" p. 115, "Nihayat al-Murad" p. 387, and Allah knows best.