M marco Joined Jun 29, 2013 Messages 2 Reaction score 0 Jun 29, 2013 #1 hi can some body guide me for getting the logical equivalence of this problem ¬(a→b) ↔ a^¬b = a→(b→a) Last edited: Jun 29, 2013
hi can some body guide me for getting the logical equivalence of this problem ¬(a→b) ↔ a^¬b = a→(b→a)
M marco Joined Jun 29, 2013 Messages 2 Reaction score 0 Jun 29, 2013 #2 ¬(a→b)= a^¬b a^¬b ↔a^¬b i dont know whats next.
C Country Boy Joined Dec 15, 2021 Messages 157 Reaction score 38 Jan 4, 2022 #3 "a→(b→a)" is a tautology since if a is true then anything implies a: both T→T and F→T are true. It is "=" to "¬(a→b) ↔ a^¬b" since that is also a tautology. If a→b is not true then a is true but b is false and so a^¬b is also true.
"a→(b→a)" is a tautology since if a is true then anything implies a: both T→T and F→T are true. It is "=" to "¬(a→b) ↔ a^¬b" since that is also a tautology. If a→b is not true then a is true but b is false and so a^¬b is also true.