query: I don't understand the truth table for logical consequence $(a \rightarrow b)$
positive_passages.docid: 578
positive_passages.text: In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?
negative_passages.docid: 93742
negative_passages.text: Show that the conditional statement is a tautology without using a truth table
negative_passages.docid: 106797
negative_passages.text: Truth Tables for Digital Circuits
negative_passages.docid: 140194
negative_passages.text: Using natural deduction to prove that $p \implies q \vdash \lnot p \lor q$
negative_passages.docid: 88104
negative_passages.text: Prove "$(p \lor q) \land (\neg p \lor r)) \rightarrow (q \lor r)$" is a tautology
negative_passages.docid: 87928
negative_passages.text: Proof of logical equivalence of biconditional and other proposition
negative_passages.docid: 5293
negative_passages.text: Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
negative_passages.docid: 70585
negative_passages.text: Why does Assuming[x > 0, TrueQ[x > 0]] return False?
negative_passages.docid: 73231
negative_passages.text: Why in implication, if premise is false then implication is true?
negative_passages.docid: 85770
negative_passages.text: What is the difference between ∀x(p(x) →q(x)) and ∀x(p(x) ∧q(x))?
negative_passages.docid: 65379
negative_passages.text: Deriving $\neg R$ from $\{R↔(R∨(P∧¬P)), R↔¬P, ¬P→(P↔(Q→Q)), P→Q\}$
negative_passages.docid: 143627
negative_passages.text: Use the Fitch system to prove the tautology (p ∨ ¬p)
negative_passages.docid: 70500
negative_passages.text: Implies ($\Rightarrow$) vs. Entails ($\models$) vs. Provable ($\vdash$)
negative_passages.docid: 35897
negative_passages.text: Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
negative_passages.docid: 32009
negative_passages.text: Prove $\;\big((p\rightarrow q) \lor (p \rightarrow r)\big) \rightarrow (q\lor r)\equiv p \lor q \lor r$ without use of a truth table.
negative_passages.docid: 52585
negative_passages.text: How to prove that $[(p \to q) \land (q \to r)] \to (p \to r)$ is a tautology without using the truth table?
negative_passages.docid: 29110
negative_passages.text: Propositional Intuitionistic Logic Question