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    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"?
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    (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"
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    (Original post by XShmalX)
    It think for "only if" both "A implies B" & "B implies A"
    :nope: 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'
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    (Original post by Clarity Incognito)
    :nope: 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?
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    (Original post by Clarity Incognito)
    :nope: 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!
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    (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".
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    (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.
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    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"
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    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.
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      (Original post by nuodai)
      A \Rightarrow B means "B only if A" or "A is sufficient for B" or "A implies B"

      A \Leftarrow 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?
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      (Original post by Kolya)
      I think you've got yourself a bit mixed up here?
      Horrifically so... corrected.
     
     
     
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