Can you prove those two equations for me ? a) a’c’+a’bc+b’c=a’+b’ b) (a’+b)’(a’+
ID: 1835487 • Letter: C
Question
Can you prove those two equations for me ?a) a’c’+a’bc+b’c=a’+b’
b) (a’+b)’(a’+c’)’(ab’c)’=0
Explanation / Answer
b) from demorgans law (a+b)' = a'b' and (ab)' =a'+b' so (a’+b)’(a’+c’)’(ab’c)’ = ab' (ac) ( a'+b+c') a*a =a and a*a'=0 => ab'c(a'+b+c') = ab'ca' +ab'cb + ab'cc' = aa'b'c+ab'bc+ab'cc' each of the terms are 0 so 0 + 0+ 0 =0 a) in boolean algebra we have a very good property that if we want simplify some expression we can replace the AND with OR and OR logic with AND and wahtever answer you get replace the AND with OR and OR logic with AND suppose here we have a’c’+a’bc+b’c replace AND with OR and OR with AND then (a'+c') . (a'+b+c) .(b'+c) = (a' + a'b+a'c+a'c'+bc')(b'+c) = a'b'+a'c+a'bc+a'b'c+a'c+a'b'c' =a'b' now replace + with . and . with + so ans is a' + b'