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Let $A$ and $B$ be arbitrary sets and consider the following two statements: \begin{gather} (x\in A)\Rightarrow (x\in B)\\ (x\in A)\Leftrightarrow (x\in B) \end{gather}

These two statements are usually worded as follows:

  1. If $x$ belongs to $A$, then $x$ belongs to $B$”
  2. “$x$ belongs to $A$ if and only if $x$ belongs to $B$”.

My questions are:

  1. Can the first statement be read as “$x$ belongs to $A$ when $x$ belongs to $B$”?
  2. Can the second statement be read as “$x$ belongs to $A$ whenever $x$ belongs to $B$”?

So, is it possible to use “when” instead of “if” and “whenever” instead of “if and only if”?

FD_bfa
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EoDmnFOr3q
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    "The street gets wet whenever/when it rains." just means that if it rains, then the street gets wet. – Pedro Mar 29 '23 at 17:06
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    "When" and "whenever" are interchangable with "if". For "iff", you could use "exactly when". – Zuy Mar 29 '23 at 17:09
  • Thank you both! – EoDmnFOr3q Mar 29 '23 at 17:11
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  • In your Question 1, you accidentally switched the two clauses. $\quad$ 2. 'Whenever' is more emphatic than, but not logically stronger than, 'when'. $\quad$ 3. 'precisely when' $\quad$ 4. There's an Answer on this site that claims that 'when' means iff, but that's probably a minority opinion.
    • – ryang Mar 29 '23 at 17:23