"I am a man, she is a woman."
Translation:Ben erkeğim, o kadın.
I'm a native speaker of German and have only recently picked up Turkish, so no authority here - but I guess "Ben erkek" literally sounds like "I, man" in English. The suffix "-im" is the equivalent of "am" ("to be" is always suffixes in Turkish, unless for some 3rd person singular cases).
The word "Adam" comes from the name "Adem", which is the name of the person thought to be the ancestor of humans. It is of Arabic origin. It is used for adult men.
The word "Erkek" indicates gender. It is of Turkish origin. Used for all men. If I give an example, it is better understood:
*I don't know that man. (O adamı tanımıyorum.)
*He is a man. (O bir erkek.)
If you use the words "kadın" and "erkek" together, do not say "adam". Because if we are talking about two genders, the word "erkek" should be used in return for the word "kadın".
*Men and women work together. (Kadınlar ve erkekler birlikte çalışırlar.)
- The man is very tired. (Adam çok yorgun.)
*The men know this job. (Adamlar bu işi biliyor.)
*Men have a beard. (Erkeklerin sakalı vardır.)
The word "bayan" was coined later. It is not included in Turkish. It is the equivalent of "Mrs". It is not used instead of gender. In the 20th century, the word "bay", which means rich in ancient Turkish, was used to address men, and the word "bayan" for women was derived from the word "bay (mr)". It is completely made up. Many women hate this word. If you use it, you can get reaction. By the way, I hate using it too. Because it's sexist.