Register to reply

DISCRETE MATH: Use rules of inference to show that...

by VinnyCee
Tags: discrete, inference, math, rules
Share this thread:
Jan25-07, 01:35 PM
P: 492
1. The problem statement, all variables and given/known data

Use rules of inference to show that if [tex]\forall\,x\,(P(x)\,\vee\,Q(x))[/tex] and [tex]\forall\,x\,((\neg\,P(x)\,\wedge\,Q(x))\,\longrightarrow\,R(x))[/tex] are true, then [tex]\forall\,x\,(\neg\,R(x)\,\longrightarrow\,P(x))[/tex] is true.

2. Relevant equations

Universal instantiation, Disjunctive syllogism, Conjunction.

3. The attempt at a solution

1) [tex]\forall\,x\,(P(x)\,\vee\,Q(x))[/tex] Premise

2) [tex]P(a)\,\vee\,Q(a)[/tex] Universal instantiation of (1)

3) [tex]\neg\,P(a)[/tex] Disjunctive syllogism of (2)

4) [tex]\forall\,x\,((\neg\,P(x)\,\wedge\,Q(x))\,\longrightarrow\,R(x))[/tex] Premise

5) [tex](\neg\,P(a)\,\wedge\,Q(a))\,\longrightarrow\,R(a)[/tex] Universal instantiation of (4)

6) [tex]R(a)[/tex] Modus Ponens of (5)

Here I am stuck, any suggestions?
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100

Register to reply

Related Discussions
DISCRETE MATH: Use math. induction to show that at least 1 integer can divide another Calculus & Beyond Homework 4
Logic: Rules of Inference Calculus & Beyond Homework 0
Simple math rules seem contradictory... General Math 6
Discrete math Calculus & Beyond Homework 3
Math Rules Chem Chemistry 12