I need help with this question please, i don't understand what the question is asking and how to go about it:

Q: Use the duality principle to find the dual of X+1=1

 

Presumably, your question is about boolean algebra.

Do you know De Morgan's Theorem?

 

Yh its boolean algebra

and yh i know De Morgans but how does it relate to my question?

 

I need help with this question please, i don't understand what the question is asking and how to go about it:

Q: Use the duality principle to find the dual of X+1=1

The first two things you need to be sure of is that you have an adequate understanding of (1) the duality principle and (2) what the "dual" of something is.

So explain, in your own words, what each of these means. You don't have to do it from memory -- use any references you want, but formulate it in your own words (that forces your mind to actually think about the concepts whereas just parroting them won't accomplish that).

 

Presumably, the X stands for an arbitrary boolean variable. Also the plus '+' sign stands for the logical OR operation. In words the expression you wrote says:

"An arbitrary boolean variable, logically OR'ed with a '1' is a '1'.

HINT:
Can you think of another boolean operation involving an "arbitrary boolean variable", and a boolean constant that is always true?

Now, if you get that far, you can verify with further research weather that expression does or does not meet the definition of a "dual".

For Example. X ^ 1 = X*
In words: X exclusive OR'ed with a 1 is the complement of X. Is that the dual you seek?
Or perhaps X ^ 0 = X
How about that one?