So am reading a book titled 'an introduction to logic', and the topic at hand is Sentential logic > Biconditionals. At one point, the author gives examples of 3 sentences that draw upon three similar though different logical arguments:
''24. The figure on the board is a triangle only if it has exactly three sides.
25. The figure on the board is a triangle if it has exactly three sides.
26. The figure on the board is a triangle if and only if it has exactly three sides.
Let T mean ‘The figure is a triangle’ and S mean ‘The figure has three sides. ''
Source: 'An introduction to Logic' by P.D Magnun - Page 27 https://textbookequity.org/Textbooks/Magnus_forallx.pdf
So basically, from what I read, 24 is the same as T -> S, 25. Is the the same as S -> T, and so basically, if 24 is 'if T then S', and 25 is 'if S then T', then where 26 is saying 'if and only if, then it's a combination of statements 24 and 25, so T implies S, S implies T, thus S and T are synonymous.
Here's the thing though, I would of thought that since the statement 'only if A, then B' infers that if A occurs, B follows, and if B occurs, then A had to have occurred prior B. So, personally, I think 24 and 26 are the same, only that 26 is a stronger statement than 24 (not logically, just persuasively, but of course I could be wrong)
So if i'm playing a game where I win 'only if I score 100 points',then if I score 100, I win, if I win, I scored 100 points.
P.S, I don't know whether this question is suited for philosophy, I've read that logic is tied into philosophy, though am also aware that this type of reasoning is also employed in mathematical proofs. If you think it's more suited for the latter, please don't downvote, but merely comment asking me to move this question.