Simplifying a logical equivalence statement without a truth table


by needshelp5
Tags: associativity, demorgan's law, logical equivalence
needshelp5
needshelp5 is offline
#1
Jan25-10, 09:37 PM
P: 1
1. The problem statement, all variables and given/known data
[(p->r) ^ (q->r)] -> (p ^ q) -> r


2. Relevant equations
anything but a truth table! laws such as (p->q)= ~(p^~q) or (p->q)=(~q->~p) might help
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
Mark44
Mark44 is offline
#2
Jan29-10, 03:50 PM
Mentor
P: 21,071
See how far you get using the relevant equations you showed. Other relevant equations that will come in handy are DeMorgan's Laws, ~(p ^ q) <==> ~p V ~q, and ~(p V q) <==> ~p ^ ~q.


Register to reply

Related Discussions
a confusion about truth table of logical implication Set Theory, Logic, Probability, Statistics 12
logical equivalence of statements with truth tables Calculus & Beyond Homework 4
Truth value of statement Calculus & Beyond Homework 4
Truth of this statement? General Physics 5