
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 20th, 2018, 02:55 PM  #1 
Newbie Joined: Sep 2018 From: United States Posts: 1 Thanks: 0  Laws of equivalence
Use equivalence laws to show that (A ∨ C) ∧ (B ∨ C) ∧ (A ∨ D) ∧ (B ∨ D) and (A ∧ B) ∨ (C ∧ D) are logically equivalent. I am trying to figure out how to go about this problem. The part that confuses me is that there are 4 separate terms. How would you apply the laws on that? 
September 20th, 2018, 04:19 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,157 Thanks: 631 
You could always write out the truth table for each expression. With 4 variables there are only $2^4 = 16$ rows. Wouldn't take long to work out the truth value of each expression for each combination of truth values.

October 20th, 2018, 02:12 PM  #3 
Member Joined: Oct 2018 From: Netherlands Posts: 39 Thanks: 3 
When you need to reduce the number of logical terms, first look at the distributive laws (in reverse direction). Triple application brings you to the Holy Land. https://en.wikipedia.org/wiki/Logical_equivalence 

Tags 
equivalence, laws 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Not sure if index laws or log laws  PGibson  Algebra  10  August 20th, 2017 10:45 PM 
Exponent laws  BreakingTheCode  Algebra  1  March 18th, 2014 09:57 PM 
Laws of Logic  FloorPlay  Applied Math  2  December 4th, 2012 01:11 PM 
absorption laws:  pappi  Applied Math  2  March 25th, 2011 01:03 AM 
Keplers laws  Alex510  Calculus  1  October 6th, 2008 08:21 PM 