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Statement -> Conditional, Converse, Inverse, Contrapositive
Gigazombie Cybermage
Registered User, __BANNED USERS regular
Registered User, __BANNED USERS regular
How do you turn a normal statement into a conditional?
"All stores are closed."
I thought the conditional would be: If they are all stores, then they are closed.
Here's what I got for my other answers.
Converse: If they are closed, then they are all stores.
Inverse: If they are not all stores, then they are not closed.
Contrapositive: If they are not closed, then they are not all stores.
I also have to show which of them is logically equivalent to the original statement. Not sure if he wants a truth table showing it or not, doesn't really give me room on the sheet to do it though.
"All stores are closed."
I thought the conditional would be: If they are all stores, then they are closed.
Here's what I got for my other answers.
Converse: If they are closed, then they are all stores.
Inverse: If they are not all stores, then they are not closed.
Contrapositive: If they are not closed, then they are not all stores.
I also have to show which of them is logically equivalent to the original statement. Not sure if he wants a truth table showing it or not, doesn't really give me room on the sheet to do it though.
Gigazombie Cybermage on
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But if you treat those as your two statements, then yeah, your other answers look right. The only way to really show which of them are equivalent is with a truth table, I think. So if you just need to give the answer, you can do the table on another page. If you have to show it, then write small :P
To help, it can all be in one truth table, you know that yeah? You don't need a separate table for each thing, just put them in different columns.
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Oh yeah, that sounds a lot better :P
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If it is a store, then it is closed. Or store -> closed.
The converse is just turning it around:
Closed -> store (if it is closed, then it is a store).
For the inverse we put "not" in front of both parts of the original:
Not store -> not closed (if it's not a store then it's not closed).
For the contrapositive, we reverse the statement and also add nots:
Not closed -> not store (if it's not closed then it's not a store).
I don't know why people bother teaching this stuff because it's pretty worthless but there you go. The only useful part is turning the original statement into a conditional but it looks like they didn't really bother teaching you how to do it. I think the best way to think about it is, "what information does the sentence give me?" Well, if all stores are closed, then we know for every X, if X is a store, then X is closed. We also know the contrapositive (for every X, if X is not closed, then X must not be a store, because all stores are closed) but presumably they wouldn't like it if you just translated the sentence directly into the contrapositive even though they are logically equivalent.