Simplify Boolean expression with De Morgan's laws

Question

I need to simplify this Boolean expression with De Morgan's laws.

¬c xor (¬b ∨ c) 

Could someone help me?

Answer 1

(accidentally made two accounts, so just responding with this one)

Ive found the best way to visualize a logic formula you do not understand is to make a table for it.

In the case of XOR, it represents One variable or another, but not both. So, lets make a table for A XOR B

A | B | Result

T | T | F    *1
T | F | T    *2
F | T | T    *3
F | F | F    *4

To generate the smallest possible result from the above table we can first take the most complex result that takes into account each option. Converting each line into a logical statement is fairly easy.

First, throw out anything that results in a False, Then take those that result in true, and convert them into a logical statement separated by 'OR's. In this case, 1 and 4 are false, and 2 and 3 are true. This means we only need to create logical statements for 2 and 3. I think how to do so would be best explained by example

Lets say X, Y, and Z are our variables, and the table gave us the following rows as true:
T | T | F    -  X & Y & ¬Z
F | T | F    - ¬X & Y & ¬Z
F | F | F    - ¬X & ¬Y & ¬Z

then to complete, we simply 'OR' them together

(X & Y & ¬Z) V (¬X & Y & ¬Z) V (¬X & ¬Y & ¬Z)

as you can see, where the variable is true, you put the variable directly in, and where it is false, you put a '¬' before the variable. The statement above basically says...

(True when X=T,Y=T,Z=F: False otherwise) OR (True when X=F,Y=T,Z=F: False otherwise) OR (True when X=F,Y=F,Z=F: False otherwise)

So finally bringing it back to our XOR the table rows are...

*2  A & ¬B
*3 ¬A & B

and are combined to be...

(A & ¬B) V (¬A & B)

So, now that you have an explanation of what to do with xor, you can apply this example to your problem, and come up with a logical statement you can use De Morgan's laws on to simplify.

Answer 2

first you have to split up xor into its basic form.

XOR represents A or B where A != B. If you can do that you should have more luck using demorgans on the whole equation