Equivalence Question between when-then statement and if then statement

In summary: This can cause confusion when reading and writing proofs. In summary, the student is trying to prove a problem where they must assume a proposition statement, but is confused about whether to assume "when p is true, then q is true" or "if p is true, then q is true". They also mention potential confusion due to language and translation issues.
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cbarker1
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TL;DR Summary
What is the equivalence between when then and if-then statement
Dear Everybody,

I am working on my homework. I am trying to prove a problem that was written by my professor in an odd way: Prove that when p is true, then q is true. Which proposition statement should I assume? I personally thought that I should assume the first one. But reading my introduction to proof writing it says "Q, when P for implication statement." Now, I am confused on what to assume?

Thanks,
Cbarker1
 
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Who wrote the book? I'm pretty sure we can assume "if" in those cases, except in case the statement is time-dependent.
 
  • #3
I forgot to add that my professor wrote the problem.
 
  • #4
I was asking because it might be a language issue. "If" in German is "wenn" so it could be a translation problem. Another, possibly more likely reason could be that "when" is commonly used in the same sense as "if", disregarding the timely connotation of "when". When it happens it does not necessarily require a time scale. It simply means if it happens.
 
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cbarker1 said:
TL;DR Summary: What is the equivalence between when then and if-then statement

Dear Everybody,

I am working on my homework. I am trying to prove a problem that was written by my professor in an odd way: Prove that when p is true, then q is true. Which proposition statement should I assume?
I can't see that "when p is true, then q is true" could possibly mean "if q, then p". Words and phrases like "assuming", "whenever", "when", "in the event that", "under the assumption that" etc. are sometimes used instead of the more formal "if".
 

FAQ: Equivalence Question between when-then statement and if then statement

What is the difference between a "when-then" statement and an "if-then" statement?

A "when-then" statement typically indicates a condition followed by a consequence that is expected to occur whenever the condition is met. In contrast, an "if-then" statement is often used to express a hypothetical scenario where the consequence will occur only if the condition is true. The primary difference lies in the implication of certainty in "when-then" versus the conditional nature of "if-then."

Are "when-then" statements always equivalent to "if-then" statements?

Not necessarily. While they can often be used interchangeably in everyday language, their logical implications can differ. "When-then" implies that the outcome is guaranteed to happen whenever the condition is met, whereas "if-then" leaves room for uncertainty about whether the condition will lead to the outcome.

Can "when-then" statements be used in formal logic?

Yes, "when-then" statements can be used in formal logic, but they are less common than "if-then" statements. In formal logic, "if-then" statements are typically represented as implications, which can be rigorously analyzed. "When-then" statements may require additional context to be formalized correctly.

In programming, how do "when-then" and "if-then" statements differ?

In programming, "if-then" statements are widely used in conditional statements to execute code based on whether a condition is true. "When-then" statements are less common but can be found in event-driven programming, where specific actions are triggered by events. The key difference is that "if-then" checks for conditions, while "when-then" responds to events.

Can both statements be used to express the same logical relationship?

In some contexts, "when-then" and "if-then" can express similar logical relationships, but they do so with different emphases. "If-then" emphasizes the conditionality and possibility, while "when-then" emphasizes certainty and inevitability. Therefore, while they may lead to similar conclusions, the nuances in meaning can affect their use in specific scenarios.

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