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September 20th, 2018, 02:55 PM   #1
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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?
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September 20th, 2018, 04:19 PM   #2
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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.
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October 20th, 2018, 02:12 PM   #3
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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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