[논리회로] 불대수 합의의정리 증명

 

(x+y)(y+z)(x’+z)

= (x+y)(0+y+z)(x'+z)

= (x+y)(xx'+y+z)(x'+z)

= (x+y)(x+y+z)(x'+y+z)(x'+z)

= (x+y)(x'+z)

 

/*

xx'+y+z = xx'+(y+z)=(x+y+z)(x'+y+z) : 분배 법칙

(x+y)(x+y+z) = x+y : 흡수 법칙

(x'+y+z)(x'+z) = x'+z : 흡수 법칙

*/

 

 

xy+yz+x'z

= xy+(x+x')yz+x'z

= xy+xyz+x'yz+x'z

= x(y*1+yz)+x'(z*1+yz)

= xy(1+z)+x'z(1+y)

= xy+x'z

 

/*

(x+x') = 1

(x+x')yz = xyz+x'yz : 분배법칙

y*1 = y

*/

 

 

조지 불(George Boole)