Substitute common sense terms. If I say “if it is an apple, it is a fruit”, does it then follow that a thing is a fruit if and only if it is an apple? No.
If B then A is the same as if X then Y is the same as if A then B. They are saying it’s the same as the OP. Changing the letters around doesn’t change the meaning since the letters are just placeholders.
Now if you said If A then B AND If B then A as one it wouldn’t be the same because A and B would have to keep the same meaning.
Lafari@lemmy.world 5 months ago
Is “If B then A” equal to “B if and only if A”?
Maddie@sh.itjust.works 5 months ago
Also no.
Lafari@lemmy.world 5 months ago
Thanks. Could you possibly elaborate? Why are they not equal?
Boinkage@lemmy.world 5 months ago
Substitute common sense terms. If I say “if it is an apple, it is a fruit”, does it then follow that a thing is a fruit if and only if it is an apple? No.
Thoth19@lemmy.world 5 months ago
No. They are effectively the same statement.
(A <=> B ) = (A=>B AND B=> A)
Rhynoplaz@lemmy.world 5 months ago
Wait. If they are effectively the same statement, wouldn’t that mean they ARE equal?
Casey_Masterpiece@lemmy.world 5 months ago
If B then A is the same as if X then Y is the same as if A then B. They are saying it’s the same as the OP. Changing the letters around doesn’t change the meaning since the letters are just placeholders.
Now if you said If A then B AND If B then A as one it wouldn’t be the same because A and B would have to keep the same meaning.
Thoth19@lemmy.world 5 months ago
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
zenharbinger@lemmy.world 5 months ago
Also, Not (A XOR B)