Comments by "Muizz" (@muizzy) on "Wendover Productions" channel.

  1. To the contrary; both doors are safe. Here's why: Let's name door 1 A, and door 2 B. We can then say denote "A is safe" as "A" and "A is deadly" as "!A" (this is logical notation). We'll use this to translate the statement given to: "If A, then !B". We'll differentiate all 4 cases of door options, and check whether the statement would be true or false. A and B: This is in conflict with "then !B", so the statement fails here. (Statement is False) A and !B: Nice! the exact statement. (Statement is True) !A and B: We only know "If A, then ...", but A is not the case here. (Statement is True) !A and !B: Same as above. (Statement is True) Now we are given the extra piece of information that the statement is false; hence the only option is "A and B"; or translating back to natural language: A is safe and B is safe.
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  2. To the contrary; both doors are safe. Here's why: Let's name door 1 A, and door 2 B. We can then say denote "A is safe" as "A" and "A is deadly" as "!A" (this is logical notation). We'll use this to translate the statement given to: "If A, then !B". We'll differentiate all 4 cases of door options, and check whether the statement would be true or false. A and B: This is in conflict with "then !B", so the statement fails here. (Statement is False) A and !B: Nice! the exact statement. (Statement is True) !A and B: We only know "If A, then ...", but A is not the case here. (Statement is True) !A and !B: Same as above. (Statement is True) Now we are given the extra piece of information that the statement is false; hence the only option is "A and B"; or translating back to natural language: A is safe and B is safe.
    2
  3. To the contrary; both doors are safe. Here's why: Let's name door 1 A, and door 2 B. We can then say denote "A is safe" as "A" and "A is deadly" as "!A" (this is logical notation). We'll use this to translate the statement given to: "If A, then !B". We'll differentiate all 4 cases of door options, and check whether the statement would be true or false. A and B: This is in conflict with "then !B", so the statement fails here. (Statement is False) A and !B: Nice! the exact statement. (Statement is True) !A and B: We only know "If A, then ...", but A is not the case here. (Statement is True) !A and !B: Same as above. (Statement is True) Now we are given the extra piece of information that the statement is false; hence the only option is "A and B"; or translating back to natural language: A is safe and B is safe.
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