Question

2. Verify, without using a truth table, if $\Gamma \models \varphi$ holds or not: a) $\Gamma = \{((d \lor s) \to p; c \to \neg p; \neg c \to e; d\}$ and $\varphi$ is $e$ b) $\Gamma = \{A \to (\neg B \lor C); (\neg D \land A) \to B; \neg E \to A\}$ and $\varphi$ is $D \lor (C \lor E)$ c) $\Gamma = \{(p \lor q) \to s; \neg p \to q, q \to \neg s \}$ and $\varphi$ is $s \land \neg q \land p$ d) $\Gamma = \Phi$ (The empty set) and $\varphi$ is $((p \lor (p \to q)) \to q)$

Name: 2 verify without using a truth table if gamma models varphi holds or not a gamma d lor s to p c to neg p neg c to e d and varphi is e b gamma a to neg b lor c neg d land a to b neg e to a an 98741
Uploaded: 2023-09-06T18:52:34-08:00
Duration: 3 min 12 s
Channel: Akash M
Description: 2 verify without using a truth table if gamma models varphi holds or not a gamma d lor s to p c to neg p neg c to e d and varphi is e b gamma a to neg b lor c neg d land a to b neg e to a an 98741

          2. Verify, without using a truth table, if $\Gamma \models \varphi$ holds or not:
a) $\Gamma = \{((d \lor s) \to p; c \to \neg p; \neg c \to e; d\}$ and $\varphi$ is $e$
b) $\Gamma = \{A \to (\neg B \lor C); (\neg D \land A) \to B; \neg E \to A\}$ and $\varphi$ is $D \lor (C \lor E)$
c) $\Gamma = \{(p \lor q) \to s; \neg p \to q, q \to \neg s \}$ and $\varphi$ is $s \land \neg q \land p$
d) $\Gamma = \Phi$ (The empty set) and $\varphi$ is $((p \lor (p \to q)) \to q)$

2 verify without using a truth table if gamma models varphi holds or not a gamma d lor s to p c to neg p neg c to e d and varphi is e b gamma a to neg b lor c neg d land a to b neg e to a an 98741

Added by Anthony B.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Akash M

09/06/2023

Step 1

The goal is to derive $\varphi$ from the premises in $\Gamma$. If we can derive $\varphi$, then $\Gamma \models \varphi$. If we cannot, then it does not hold. Let's analyze each sub-problem. **Part a)** $\Gamma = \{((d \lor s) \to p), (c \to \neg p), (\neg c \to Show more…

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2. Verify, without using a truth table, if $\Gamma \models \varphi$ holds or not: a) $\Gamma = \{((d \lor s) \to p; c \to \neg p; \neg c \to e; d\}$ and $\varphi$ is $e$ b) $\Gamma = \{A \to (\neg B \lor C); (\neg D \land A) \to B; \neg E \to A\}$ and $\varphi$ is $D \lor (C \lor E)$ c) $\Gamma = \{(p \lor q) \to s; \neg p \to q, q \to \neg s \}$ and $\varphi$ is $s \land \neg q \land p$ d) $\Gamma = \Phi$ (The empty set) and $\varphi$ is $((p \lor (p \to q)) \to q)$