ok given the boolean expression F= X'Y+XYZ'
a. derive an algebraic expression for F'
ive found the one above
F= X'Y+XYZ'
=(X'+Y)(X+Y+Z')
=(X'+Y')(X'+Y'+Z)
THEREFORE F'= (X+Y')(X'Y'+Z)
NOW SHOW THAT F.F'=0
AND F+F'=1
THIS IS WHERE I AM AT PAUSE..
ok given the boolean expression F= X'Y+XYZ'
a. derive an algebraic expression for F'
ive found the one above
F= X'Y+XYZ'
=(X'+Y)(X+Y+Z')
=(X'+Y')(X'+Y'+Z)
THEREFORE F'= (X+Y')(X'Y'+Z)
NOW SHOW THAT F.F'=0
AND F+F'=1
THIS IS WHERE I AM AT PAUSE..
This is wrong. The first line is false when all variables are false, but the second line is true.F= X'Y+XYZ'
=(X'+Y)(X+Y+Z')
I don't see how to explain this either.=(X'+Y')(X'+Y'+Z)
Should be: F' = (X + Y')(X' + Y' + Z).THEREFORE F'= (X+Y')(X'Y'+Z)
If you multiply this by F and open all parentheses, each term will have complementary literals (like X and X'), so the product is false.
One gets F + F' = 1 by apply De Morgan's law to FF' = 0.