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September 20th, 2018, 01:55 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, 03:19 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,311 Thanks: 706 
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, 01:12 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 

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