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 and only if is a biconditional. “b if and only if a” means “if b then a” AND “b only if a”. B only if A here means “It is an apple only if is a fruit”, in other words, “if it is a fruit, it could only be an apple.” Which ain’t right.
Lafari@lemmy.world 11 months ago
Thanks. Could you possibly elaborate? Why are they not equal?
Boinkage@lemmy.world 11 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.
Rhynoplaz@lemmy.world 11 months ago
Better read that one again.
If Apple then fruit. Is Apple ONLY if it’s a fruit.
This one actually checks out.
Boinkage@lemmy.world 11 months ago
If and only if is a biconditional. “b if and only if a” means “if b then a” AND “b only if a”. B only if A here means “It is an apple only if is a fruit”, in other words, “if it is a fruit, it could only be an apple.” Which ain’t right.