The complement of the given expressions is:
(a) xy + x'y
(b) a'c'a'b abc + a'b'c + ab'c'
(c) z(v'w + xy) + z'
How to solve
Let's find the complement of the following expressions:
(a) xy' + x'y
(b) (a + c)(a + b')(a' + b + c')
(c) z + z'(v'w + xy)
The complement of an expression is the expression that evaluates to true when the original expression evaluates to false, and vice versa.
Steps to solve:
(a) xy' + x'y
The complement of xy' is x'y, and the complement of x'y is xy. Therefore, the complement of xy' + x'y is xy + x'y.
(b) (a + c)(a + b')(a' + b + c')
The complement of (a + c) is a'c', the complement of (a + b') is a'b, and the complement of (a' + b + c') is abc + a'b'c + ab'c'. Therefore, the complement of (a + c)(a + b')(a' + b + c') is a'c'a'b abc + a'b'c + ab'c'.
(c) z + z'(v'w + xy)
The complement of z is z', and the complement of z'(v'w + xy) is z(v'w + xy). Therefore, the complement of z + z'(v'w + xy) is z(v'w + xy) + z'.