Tagged Questions

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Correctly understanding truth table problem?

I'm typing up a solution set for an "intro to proof" course. One of the problems asks the student to "construct a truth table for $(P \implies Q) \implies (\neg P)$." I interpreted this as requesting ...
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Prove or refute: $A_1,\ldots,A_n\vdash_{CPL} B \iff (A_1 \wedge \ldots \wedge A_n)\vdash_{CPL} B$

Need to prove or refute: $A_1, \ldots, A_n \vdash_{\rm CPL} B \iff A_1 \land\dots\land A_n \vdash_{\rm CPL} B$ Since we have $\iff$ operator, we have to deal with to directions. Let's begin from ...
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Prove or refute contingent: If A implies B is contingent, then B is too

The question is: If $A, A \to B$ are contingent, then so is $B$ $A, A \to B$ (implies) is a contingent, but how exactly to show «so is $B$»? If I'm using a truth table, how should I show that ...
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Prove/refute: Every tautology is contingent

I'm asking to prove/refute the following statement: Every tautology is contingent. According to definition of contingent: A statement that is neither self-contradictory nor tautological is ...
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Rooted Trees & Induction

So I am a little stumbled upon this question: A full binary tree is a rooted tree where each leaf is at the same distance from the root and each internal node has exactly two children. Inductively, a ...
107 views

Rules of inference proofs

I have the following: Premise: {$p \lor q, q\rightarrow r,p \land s \rightarrow t, \lnot r, \lnot q \rightarrow u \land s$}, conclusion: $t$ I'm having a real hard understanding how to prove the ...
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Verify these logical equivalences by writing an equivalence proof?

I have two parts to this question - I need to verify each of the following by writing an equivalence proof: $p \to (q \land r) \equiv (p \to q) \land (p \to r)$ $(p \to q) \land (p \lor q) \equiv q$ ...
338 views

proof of validity of tautology in first order logic

Every first-order logic formula which has a tautological shape in propositional logic is a valid formula. Will it be possible to give a formal proof for the above ? Thanks and Regards.
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How can I progress this derivation?

I'm learning propositional calculus in a discrete mathematics course. I'm trying to kick the habit of using axioms like equations and now I'm a little stuck and could use a nudge. Using a compact ...
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Does this proof using Novikov axiomatic propositional logic hold?

This question seems absolutely elementary but I'm having a hard time completing the proof, in fact I may have taken a bit of a left turn on it or I may be improperly applying axioms all together. ...