How do i say "for every x, show that P(x) is true"?

Question

i've been learning japanese for 2 and a half years now. for a few weeks/months now, i'm taking notes in japanese.

Listening to the teacher in french and taking notes in japanese my be challenging at times, but it's increadibly stimulating and rewarding, given that it was totally impossible not that long ago.

Yet i cannot find a translation for the statement : "for all x, show that P(x) is true", something like that.

It's especially the "show that" that i'm not sure how to properly translate. ”全てのxについて、xはP(x)である”…「を証拠立てる」・「を証明する」… or anything else

Thank you

Answer 1

証拠立てる is virtually never used in mathematical articles. I would translate it like so:

• すべてのxに対してP(x)が真であることを示せ。
• すべてのxについてP(x)が成り立つことを証明せよ。