My Math Forum Laws of equivalence

 Probability and Statistics Basic Probability and Statistics Math Forum

 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

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