[Math] Applying De Morgan’s Laws

logic

I have recently started working on De Morgan's laws and Boolean algebra at school, and i just cant seem to get my head around it. We were given a worksheet to complete, here are some of the questions:

1) Using De Morgan's Laws, simplify the following: Not(A AND B) OR A

2) Using De Morgan's Laws, show that A + A.B = A

I've done some research my self and have tried to understand it, but i just cant, I do understand the terms such as and,or not etc. but i don't understand how De Morgan's laws work or how to apply them.

Sorry if the title is wrong or misleading to what im asking, i don't use this site much and thanks in advance for any answers.

Best Answer

1) Using De Morgan's Laws, simplify the following: Not(A AND B) OR A

The trick for this one is as follow:

    NOT(A AND B) OR A
<=> NOT(A) OR NOT(B) OR A      // The trick is here. Literally De Morgan's law.
<=> (NOT(A) OR A) OR NOT(B)
<=> TRUE OR NOT(B)
<=> TRUE

So this (1) is a tautology.

2) Using De Morgan's Laws, show that A + A.B = A

And for this one, here is the trick:

    A + A.B
<=> A OR (A AND B)       
<=> A AND (TRUE OR B)    // The trick is here. like in Math:  x + (x*y) = x*(1+y)
<=> A AND TRUE
<=> A

I hope this help.

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