Question

2.25 Given the function f (x, y,z) = xy + yz write f (x, y,z) as a sum of minterms and as a product of maxterms.

Answer 1

f(x, y, z) = xy + yz
sum of minterms:
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f(x, y, z)
= xy + yz
= xy(z + z') + (x + x')yz
= xyz + xyz' + xyz + x'yz
= xyz + xyz' + x'yz
Answer: xyz + xyz' + x'yz

product of maxterms:
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f(x, y, z)
= xy + yz
= y(x + z)
= (x'+y+z') (x'+y+z) (x+y+z') (x+y+z) (x+y'+z) (x+y+z)
= (x'+y+z') (x'+y+z) (x+y+z') (x+y+z) (x+y'+z)
Answer: (x'+y+z') (x'+y+z) (x+y+z') (x+y+z) (x+y'+z)