Lafari@lemmy.world to No Stupid Questions@lemmy.world · 8 months agoIs "If A then B" equal to "B if and only if A"?message-squaremessage-square40fedilinkarrow-up138arrow-down110
arrow-up128arrow-down1message-squareIs "If A then B" equal to "B if and only if A"?Lafari@lemmy.world to No Stupid Questions@lemmy.world · 8 months agomessage-square40fedilink
minus-squareLafari@lemmy.worldOPlinkfedilinkarrow-up3arrow-down4·8 months agoIs “If B then A” equal to “B if and only if A”?
minus-squareIt's Maddie!@sh.itjust.workslinkfedilinkEnglisharrow-up12arrow-down1·8 months agoAlso no.
minus-squareThoth19@lemmy.worldlinkfedilinkarrow-up5arrow-down2·8 months agoNo. They are effectively the same statement. (A <=> B ) = (A=>B AND B=> A)
minus-squareRhynoplaz@lemmy.worldlinkfedilinkarrow-up3·8 months agoWait. If they are effectively the same statement, wouldn’t that mean they ARE equal?
minus-squareThoth19@lemmy.worldlinkfedilinkarrow-up1·8 months agoI mean it is the definition of “if and only if”. And by commutativity we also know that A iff B is equal to B iff A
No
Is “If B then A” equal to “B if and only if A”?
Also no.
No. They are effectively the same statement.
(A <=> B ) = (A=>B AND B=> A)
Wait. If they are effectively the same statement, wouldn’t that mean they ARE equal?
I mean it is the definition of “if and only if”. And by commutativity we also know that A iff B is equal to B iff A
Also, Not (A XOR B)