Do (A implies B) and (A implies notB) contradict each other? Right, I do have some familiarity with logic gates. Are any of those useful logic paths nonsensical? Genuine question... — Janus
Well... yes, kind of.
From falsehood, anything follows. Have you ever heard of this? This example before us is a great example of that.
You think if a then b, and if a then not b contradict each other.
Many other posters think they don't contradict each other, BUT with the caveat that if they're both valid statements, A must be false.
If a is false, and "from falsehood, anything follows", then (if a, then anything) fits. Replace anything with b, replace it with not b, replace it with a snail with a tophat, replace it with à̶̙̦͔́̀b̴͈̼̞̓͘y̵̝̣̳̲̟̤͑̏̈́͝ş̷̭̼͖͓̼̈̿̈́͐͐̃̕ș̶̡̲̘̯́́̋̄͘͜ä̵̉̓͊̋͜l̸̯͛̀̒̕ ̷̞͎͔̱͛̕d̴̪̬̻̠͕̋̃͗̾̉ẹ̴̪̭̌̒͝ś̷̢̢̢͔͉͎̄̿p̸̨͎̘̼̬̼͇̓͌̊ā̵̢̤̗͌i̴̡̤̹̘̰̿͜͝r̴͉͙̣̍̂̈́̓̄̚...
As long as A is false, "if a then anything" obtains. You can verify this with the truth table. And this is where your sense of nonsense comes in. Do you see?