Thursday, July 9, 2009

Physical Interpretation of DeMorgan's law

I am asking you what is De Morgan's law. This may be the answer.
If A and B are two events,

(A+B)' = A' . B' and (A.B)' = A' + B'

(Here the operator ' represents the compliment of the operand. That is If A is 'yes' then A' is 'no' and if A is 1 then A' is 0 and vice versa). I assume you have basic knowledge of Boolean algebra. Now I am giving a physical interpretation of the law which is very useful in analising the law.

Consider first law,

(A+B)' = A' . B'

Here '+' is OR operator. That is A or B. Let Y be an event of shutting down your computer. You can do it in two ways and B.

A=>shutdown manually by pressing the power button of CPU.
B=>click 'shtdown' using your mouse.

Then,
Y=A + B ie, Y= A OR B

Another iterpretation is that, you can turn off your computer by either clicking 'sht down' or by pressing power button. If any one event occured, the computer turns off. ie, Y become true.

One day, your friend came to your home and want to learn about computer. He did something in your computer in order to turn off.Unfortunately, the computer didn't turn off. He reported you in the other room. Then you think in this way, what may be the reason why the computer didn't shut down. The output occured is Y'. ie, computer didn't turned off.

Then from the previous equation,

Y' = (A+B)'
Applying De Morgan's law,
Y' = A' . B'

Here the interpretation is that, The event A is false and event B is false. ie, he neither clicked 'shutdown' nor pressed power button.

Take De Morgan's second law (A . B)' = A' + B'
Consider two dependent events. For example,
let A and B be two dependent events. If your friend dont know how to call someone using a coinbox telephone. The procedure written on the side of the machine is first put the coin and then dial the number. They are dependent events.
A => Put the coin.
B => Dial the number.

Here the output Y is to call somone successfully. ie Y = A.B
(Here A.B is not equal to B.A which is another boolean theorm. Here just don't think about it.It will be explained later)
Unfortunately, your friend could not call the other. He asked for help. Then you analise the problem why he didn't call.

Y' = (A . B)'
By, De Morgan's law,
Y' = A' + B'

ie, he either didn't put the coin or dial the number properly. The above example is conditional events.

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