たとえ, coming from 例(たと)える, a る - Verb meaning ‘to speak figuratively’, is a word in Japanese that is often used with ても (or でも), in order to present possibilities. たとえ is primarily seen at the beginning of a sentence, before some kind of possibility, comparison, or supposition will be stated.
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空手(からて)ではたとえ試合(しあい)で勝(か)っても、ガッツポーズをしてはいけない。
Even if you win in a karate competition, you should not celebrate visibly.
たとえ暑(あつ)くても、虫(むし)が入(はい)ってくるのでこの窓(まど)は開(あ)けないで下(くだ)さい。
Even if it is hot, bugs will come in, so please do not open this window.
たとえ好(す)きでも、そんなことをされたら、嫌(きら)いになる。
Even if I like them, if someone says such a thing, I will start to dislike them.
たとえ電車(でんしゃ)でも30分(ぷん)はかかる。
Even by train, it will take at least 30 minutes.
たとえ tends to be used to present situations where ‘even if they were true, (B) still may/may not happen’. This is called a ‘contrastive’ example.
もし on the other hand tends to be used for examples in which (A) will directly result in (B). This is called a ‘resultative’ example.
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たとえ来年(らいねん)までに完成(かんせい)したとしても、中(なか)に入(はい)る店(みせ)が決(き)まっていないから来年(らいねん)中(じゅう)にはオープンされないだろう。
Even if it is completed by next year, the shops that it is going in have not been decided, so it is unlikely that they will open next year.
もし今年(ことし)中(じゅう)にモールの工事(こうじ)が終(お)わったら、来年(らいねん)の頭(あたま)にはオープンするはず。
If the construction for the mall finishes within this year, it should open at the beginning of next year.