▲ 40 ▼ Is "If A then B" equal to "B if and only if A"? (lemmy.world) submitted 2 years ago by Lafari@lemmy.world to c/nostupidquestions@lemmy.world 60 comments fedilink hide all child comments
[–] Maddie@sh.itjust.works 14 points 2 years ago (1 child) Also no. permalink fedilink source parent hideshow 2 child comments replies: [–] Lafari@lemmy.world [S] 3 points 2 years ago (1 child) Thanks. Could you possibly elaborate? Why are they not equal? permalink fedilink source parent hideshow 2 child comments replies: [–] Boinkage@lemmy.world 7 points 2 years ago* (1 child) 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. Lots of other things are fruit without being an apple. permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 0 points 2 years ago (1 child) Better read that one again. "If B then A" ... "B if and only if A"? If Apple then fruit. Is Apple ONLY if it's a fruit. This one actually checks out. permalink fedilink source parent hideshow 2 child comments replies: [–] Boinkage@lemmy.world 4 points 2 years ago* (last edited 2 years ago) (1 child) 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. B -> A (if B, then A) (if apple, then fruit, correct) B <-> A (B if and only if A) (if apple, then fruit, AND if fruit, then apple, incorrect). permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 3 points 2 years ago (2 children) Gotcha. I was reading it aloud: "It's an Apple if and only if it's a fruit." which isn't wrong, but I guess the technical definition of "If and only if" assumes more than the words imply. permalink fedilink source parent hideshow 4 child comments replies: [+] hornface@fedia.io 3 points 2 years ago* (last edited 10 months ago) [deleted] permalink fedilink source parent [–] Boinkage@lemmy.world 1 point 2 years ago* I agree, if and only if trips me up too and it doesn't fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way. permalink fedilink source parent
[–] Lafari@lemmy.world [S] 3 points 2 years ago (1 child) Thanks. Could you possibly elaborate? Why are they not equal? permalink fedilink source parent hideshow 2 child comments replies: [–] Boinkage@lemmy.world 7 points 2 years ago* (1 child) 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. Lots of other things are fruit without being an apple. permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 0 points 2 years ago (1 child) Better read that one again. "If B then A" ... "B if and only if A"? If Apple then fruit. Is Apple ONLY if it's a fruit. This one actually checks out. permalink fedilink source parent hideshow 2 child comments replies: [–] Boinkage@lemmy.world 4 points 2 years ago* (last edited 2 years ago) (1 child) 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. B -> A (if B, then A) (if apple, then fruit, correct) B <-> A (B if and only if A) (if apple, then fruit, AND if fruit, then apple, incorrect). permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 3 points 2 years ago (2 children) Gotcha. I was reading it aloud: "It's an Apple if and only if it's a fruit." which isn't wrong, but I guess the technical definition of "If and only if" assumes more than the words imply. permalink fedilink source parent hideshow 4 child comments replies: [+] hornface@fedia.io 3 points 2 years ago* (last edited 10 months ago) [deleted] permalink fedilink source parent [–] Boinkage@lemmy.world 1 point 2 years ago* I agree, if and only if trips me up too and it doesn't fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way. permalink fedilink source parent
[–] Boinkage@lemmy.world 7 points 2 years ago* (1 child) 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. Lots of other things are fruit without being an apple. permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 0 points 2 years ago (1 child) Better read that one again. "If B then A" ... "B if and only if A"? If Apple then fruit. Is Apple ONLY if it's a fruit. This one actually checks out. permalink fedilink source parent hideshow 2 child comments replies: [–] Boinkage@lemmy.world 4 points 2 years ago* (last edited 2 years ago) (1 child) 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. B -> A (if B, then A) (if apple, then fruit, correct) B <-> A (B if and only if A) (if apple, then fruit, AND if fruit, then apple, incorrect). permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 3 points 2 years ago (2 children) Gotcha. I was reading it aloud: "It's an Apple if and only if it's a fruit." which isn't wrong, but I guess the technical definition of "If and only if" assumes more than the words imply. permalink fedilink source parent hideshow 4 child comments replies: [+] hornface@fedia.io 3 points 2 years ago* (last edited 10 months ago) [deleted] permalink fedilink source parent [–] Boinkage@lemmy.world 1 point 2 years ago* I agree, if and only if trips me up too and it doesn't fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way. permalink fedilink source parent
[–] Rhynoplaz@lemmy.world 0 points 2 years ago (1 child) Better read that one again. "If B then A" ... "B if and only if A"? If Apple then fruit. Is Apple ONLY if it's a fruit. This one actually checks out. permalink fedilink source parent hideshow 2 child comments replies: [–] Boinkage@lemmy.world 4 points 2 years ago* (last edited 2 years ago) (1 child) 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. B -> A (if B, then A) (if apple, then fruit, correct) B <-> A (B if and only if A) (if apple, then fruit, AND if fruit, then apple, incorrect). permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 3 points 2 years ago (2 children) Gotcha. I was reading it aloud: "It's an Apple if and only if it's a fruit." which isn't wrong, but I guess the technical definition of "If and only if" assumes more than the words imply. permalink fedilink source parent hideshow 4 child comments replies: [+] hornface@fedia.io 3 points 2 years ago* (last edited 10 months ago) [deleted] permalink fedilink source parent [–] Boinkage@lemmy.world 1 point 2 years ago* I agree, if and only if trips me up too and it doesn't fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way. permalink fedilink source parent
[–] Boinkage@lemmy.world 4 points 2 years ago* (last edited 2 years ago) (1 child) 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. B -> A (if B, then A) (if apple, then fruit, correct) B <-> A (B if and only if A) (if apple, then fruit, AND if fruit, then apple, incorrect). permalink fedilink source parent hideshow 2 child comments replies: [–] Rhynoplaz@lemmy.world 3 points 2 years ago (2 children) Gotcha. I was reading it aloud: "It's an Apple if and only if it's a fruit." which isn't wrong, but I guess the technical definition of "If and only if" assumes more than the words imply. permalink fedilink source parent hideshow 4 child comments replies: [+] hornface@fedia.io 3 points 2 years ago* (last edited 10 months ago) [deleted] permalink fedilink source parent [–] Boinkage@lemmy.world 1 point 2 years ago* I agree, if and only if trips me up too and it doesn't fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way. permalink fedilink source parent
[–] Rhynoplaz@lemmy.world 3 points 2 years ago (2 children) Gotcha. I was reading it aloud: "It's an Apple if and only if it's a fruit." which isn't wrong, but I guess the technical definition of "If and only if" assumes more than the words imply. permalink fedilink source parent hideshow 4 child comments replies: [+] hornface@fedia.io 3 points 2 years ago* (last edited 10 months ago) [deleted] permalink fedilink source parent [–] Boinkage@lemmy.world 1 point 2 years ago* I agree, if and only if trips me up too and it doesn't fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way. permalink fedilink source parent
[+] hornface@fedia.io 3 points 2 years ago* (last edited 10 months ago) [deleted] permalink fedilink source parent
[–] Boinkage@lemmy.world 1 point 2 years ago* I agree, if and only if trips me up too and it doesn't fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way. permalink fedilink source parent