How do you say "if and only if" in Japanese?

Question

I would like to know how to express mandatory conditions in Japanese. Since Japanese distinguishes between different types of languages, I should probably ask more precisely:

What is the right way to express equivalence statements (the kind a mathematician might make) such as "The equation is satisfied if and only if a>b"?

How do you express that you're going to do or that something will happen, only if some condition is satisfied? ("I'll only go if you buy me an ice.", "The plant will only grow if it is watered regularly.")

The last paragraph (usual conditionals) is quite far removed from the question about the technical language ("if and only if"). There are several ways of expressing conditionals, and we have many questions about them (click on the [conditionals] tag to find them). I suggest you focus your question on the first part. — Earthliŋ, Feb 15 '16 at 18:55
I'm not confident enough about this as an answer, but I think that pattern is ～さえ～ば. 植物に水*さえ*やれ*ば*成長する. This pattern implies "if", but not sure about the "only if". — istrasci, Feb 15 '16 at 19:02

score 11 · Accepted Answer · edited Jun 17 '20 at 08:18

11

Two common ways of translating "if and only if" use the terms 必要十分条件 ("necessary and sufficient condition") and 同値 ("equivalence").

a > b は式 (15) である為の必要十分条件である。
Equation (15) holds if and only if a > b.

式（15）と「a>b」とは同値である。
Equation (15) is equivalent to a > b.

edited Jun 17 '20 at 08:18

Community

1

answered Feb 15 '16 at 19:23

Earthliŋ

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否｛ひ｝定｛てい｝排｛はい｝他｛た｝的｛てき｝論｛ろん｝理｛り｝和｛わ｝ if you want to write your logic in 漢文 :) This is the full name for an XNOR logic gate, which has the same operation as an iff statement. – a20 Jun 01 '20 at 16:44

broccoli facemask · Answer 2 · 2016-02-15T19:43:40.463

5

if and only if (= iff)

a > b の時、（そして／かつ）その時に限り等式が成立する。
The equation is satisfied if and only if a > b.
only ... if
- ～なければ～ない (colloquially ～なきゃ～ない or ～なけりゃ～ない)
  ≈ ～ないなら～ない
  
  アイスを買ってくれなきゃ行かない。
  I'll only go if you buy me an ice.
- ～ないと～ない
  
  この植物は定期的に水をやらないと育たない。
  The plant will only grow if it is watered regularly.
- The difference between them is, in short, you can't use the latter if your(= the speaker's) will intervenes.

edited Feb 15 '16 at 19:43

answered Feb 15 '16 at 19:09

broccoli facemask

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I thought that the technical translation usually involves 必要十分(条件) (or sometimes 同値 "equivalent"). – Earthliŋ Feb 15 '16 at 19:13
@Earthliŋ Yes, AとBは同値 would be shorter, but you can't put it into this word order. This expression is a mouthful, yet fixed. – broccoli facemask Feb 15 '16 at 19:16

How do you say "if and only if" in Japanese?

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