1) He acknowledged that he is your inferior .

他承认他不及你。
2) He acknowledged himself to be my inferior.

他承认不及我。
3) He simply won't admit it.

他死活不承认。
4) No; that was something he would never admit!

他抵死不承认的!
6) Does he know you?

他认识你吗?
参考词条