// Define the values of A and B const A = false; // A must be false for both implications to be true const B = true; // B can be any value, but it doesn't matter because A is false // Logical implication function function implies(p, q) { return !p || q; } // Check the implications const A_implies_B = implies(A, B); // A implies B const A_implies_notB = implies(A, !B); // A implies not B // Output the results console.log(`A: ${A}`); console.log(`B: ${B}`); console.log(`A implies B: ${A_implies_B}`); console.log(`A implies not B: ${A_implies_notB}`); // Check if both implications are true const result = A_implies_B && A_implies_notB; console.log(`(A implies B) and (A implies not B): ${result}`);
A contradiction is of the form "P ^ ~P" — Moliere
A contradiction is an assertion of Propositional Logic that is false in all situations; that is, it is false for all possible values of its variables. — Tautologies and Contradictions
Can anyone think up a real world example where you would point out that A implies both B and not-B except for saying something along the lines of:
"A implies B and not-B, therefore clearly not-A." — Count Timothy von Icarus
Can anyone think up a real world example where you would point out that A implies both B and not-B except for saying something along the lines of:
"A implies B and not-B, therefore clearly not-A." — Count Timothy von Icarus
A real world example is often hard to parse into material implication -- sometimes, yes, but sometimes it's hard -- the conjuncts of disjuncts, while they can be claimed, is even rarer :D
Though after we dismiss "B and not-B" as always false, we can see that the truth of the proposition will only rely upon A, since "implies" is logically equivalent to "not-A or (B and not-B)", and the truth of a disjunct is true if one of the propositions is true -- so if not-A is true then it is true, and if not then it is false -- since not all results in the truth-table are false it is not a contradiction. — Moliere
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