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# A if B? A only if B? Watch

1. Hi guys

OK sorry for another really embarrassing maths question but I would really appreciate it if you could just confirm something for me

I'm fairly sure that if A and B are 'statements' then: A if B means "B implies A" (I hope!)

But what about A only if B? Does this actually mean "A implies B"?
2. (Original post by jamesair99)
Hi guys

OK sorry for another really embarrassing maths question but I would really appreciate it if you could just confirm something for me

I'm fairly sure that if A and B are 'statements' then: A if B means "B implies A" (I hope!)

But what about A only if B? Does this actually mean "A implies B"?
It think for "only if" both "A implies B" & "B implies A"
3. (Original post by XShmalX)
It think for "only if" both "A implies B" & "B implies A"
A, if, and only if, B is equivalent to A <=> B

(Original post by jamesair99)
Hi guys

OK sorry for another really embarrassing maths question but I would really appreciate it if you could just confirm something for me

I'm fairly sure that if A and B are 'statements' then: A if B means "B implies A" (I hope!)

But what about A only if B? Does this actually mean "A implies B"?
Yeah, it does, it might be easier to think of 'A only if B' as 'not B implies not A' depending on the statements one is using. 'not B => not A' is the contrapositive of 'A=> B'
4. (Original post by Clarity Incognito)
A, if, and only if, B is equivalent to A <=> B

Yeah, it does, it might be easier to think of 'A only if B' as 'not B implies not A' depending on the statements one is using. 'not B => not A' is the contrapositive of 'A=> B'
But A <=> B means they both imply each other doesn't it?
5. (Original post by Clarity Incognito)
A, if, and only if, B is equivalent to A <=> B

Yeah, it does, it might be easier to think of 'A only if B' as 'not B implies not A' depending on the statements one is using. 'not B => not A' is the contrapositive of 'A=> B'
This is very useful indeed. Thank you so much!
6. (Original post by XShmalX)
But A <=> B means they both imply each other doesn't it?

Yes, but that's not what we've got here.

" A <=> B" in English is "A if, and only if, B".
7. (Original post by XShmalX)
But A <=> B means they both imply each other doesn't it?
Uh huh, but you said that A, only if B is equivalent to A <=> B but it's not.
8. means "A only if B" or "A is sufficient for B" or "A implies B"

means "A if B" or "A is necessary for B" or "A is implied by B"

means "A if and only if B" or "A is sufficient and necessary for B" or "A is equivalent to B"
9. A if B means the same as If B then A; which means, if there is B then there must/necessary be A; meaning B implies A but not the other way around.

A only if B, means if A there must be B; meaning A implies B but not the other way around.
10. (Original post by nuodai)
means "B only if A" or "A is sufficient for B" or "A implies B"

means "A if B" or "B is necessary for A" or "A is implied by B"
I think you've got yourself a bit mixed up here?
11. (Original post by Kolya)
I think you've got yourself a bit mixed up here?
Horrifically so... corrected.

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