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A if B? A only if B?

Hi guys

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

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"?

Reply 1

XShmalX

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 :tongue:

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"

Reply 2

Clarity Incognito

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 :tongue:

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'

Reply 3

XShmalX

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?

Reply 4

jamesair99

Original post by Clarity Incognito

This is very useful indeed. Thank you so much!

Reply 5

ghostwalker

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".

Reply 6

Clarity Incognito

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.

Reply 7

nuodai

A \Rightarrow B

means "A only if B" or "A is sufficient for B" or "A implies B"

A \Leftarrow B

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

A \Leftrightarrow B

means "A if and only if B" or "A is sufficient and necessary for B" or "A is equivalent to B"

(edited 13 years ago)

Reply 8

0011

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.