How to Prove De Morgan's Laws

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To prove De Morgan's laws, create tables that compare logic situations with P and Q variables. Use logic tables to determine the truth of different De Morgan laws with information from a tutor in this free video on math and logic.

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Video Transcript

Hi my name is Samir Malik, I'm a private tutor for middle school and high school students, today we're going to prove DeMorgan's law. And I will illustrate that with some examples for you. Now the first point, first law states, not P and Q, which means not P or Q. So for example, when you have P and Q both together this would be false. Because we have both P and Q together, and the law states not P and Q, so this first table is false. Now the second one we have not P, but we do have the Q. So because we do not have the P, but we do have the Q, then the state is true. Because they're saying for this equation, not P and Q. For the second we have not Q, but we do have P, so that is true. And for the third one we have not P and not Q, so that is also true for our first law. Moving on to the second law we have not P or Q. So in other words neither P or Q can be in our equation here. So here we have a P and we have a Q so it's false. Here we do not have a P, but we do have a Q, so it's still false. For here we do not have the Q, but we do have the P, so it's still false, because we are not allowed to have P or Q. And for the last one we do not have P and we do not have Q, so that makes the second law true, based on this diagram that I've illustrated for you. So these diagrams show us how DeMorgan's law works, and how we can prove his laws to be correct. So from these three equations we are able to understand, and were able to see how De-Morgan's law works, and we were also able to prove it using the tables which I created for you.


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