Taller - Algebra BooleanaTaller- Algebra BooleanaSimplificar las siguientes funciones de conmutacin utilizando el lgebra de Boole.1. Distributiva~a~bc+~ab~c+~abc+ab~c~ac+~ab~c+ab~cDistributiva~ac+b~c2.Complementoa~bc(~b+a)b0+~ab~ab3.De Morgan~(a+b)~a~b~(~a~bc+~a+~bd+~c~d)De Morgan~(a+b)~a~b~(~a~bc+~a+~bd+~c~d)Absorcin~a~bc+~a+~bd+~c~d~a+~bd+~c~d~(~a+~bd+~c~d)De Morgana(b+~d)(c+d)Distributivaab(c+d)+a~d(c+d)DistributivaAb(c+d)Abc+abdAbc+abd+a~d(c+d)Distributivaa~d(c+d)a~dc+a~ddabc+abd+a~dc+a~ddComplementoa~ddabc+abd+a~dc+0abc+abd+a~dc4.Distributivaa~b(c+bd)a~bc+a~bbd(a~bc+a~bbd+~a~b)cDistributivaa~b(c+bd)a~bc+a~bbd(a~bc+a~bbd+~a~b)cComplemento a~bbd(a~bc+0+~a~b)c(a~bc+~a~b)cDistributiva(a~bc+~a~b)ca~bcc+~a~bcidenpotenciaa~bcca~bca~bc+~a~bcidenpotenciaa~bcca~bca~bc+~a~bcDistributivaa~bc+~a~bc~bc5.De Morgan~(b+c)~b~ca~b+a~b~c+b~(b+c)De Morgan~(b+c)~b~ca~b+a~b~c+b~b~cComplementob~b~ca~b+a~b~c+0Absorcina~b+a~b~ca~b6.De Morgan~(ac)~a+~c(da(b+~a+~c)+ ~(ac))bcDistributivada(b+~a+~c)dab+da~a+da~c(dab+da~a+da~c+~(ac))Complementoda~a(dab+0+da~c+~(ac))bcDe Morgan~(ac)~a+~c(dab+da~c+~a+~c)bcAbsorcion Dab+da~c+~a+~cDab+~a+~c(dab+~a+~c)bcDistributiva(dab+~a+~c)bcdabbc+~abc+~cbcidenpotenciadabbcdabcdabc+~abc+~cbcComplemento~cbcdabc+~abc+0dabc+~abc7.De Morgan~(ab)~a+~b~a+~b+~(ac)+ ~a~b~cDe Morgan~(ac)~a+~c~a+~b+~a+~c+~a~b~cIdenpotencia~a+~b+~a+~c+~a~b~c~a+~b+~c+~a~b~cAbsorcin~a+~b+~c8.a~bc(ad+cde)+a~cDistributivaa~bc(ad+cde)a~bcad+a~bccde+a~cIdenpotenciaa~bccdea~bcad+a~bcde+a~c9.De Morgan ~(~a~c)a+cabc+a~b(a+c)Distributivaa~b(a+c)a~ba+a~bcabc+a~ba+a~bcIdenpotenciaa~baa~babc+a~b+a~bcAbsorcina~b+a~bca~babc+a~c10.Asociacin(ab+a~c)+ ~bAb+a~c+~b~(ab+a~c+~b)De Morgan~(ab+a~c+~b)(~a+~b)( ~a+c)bDistributiva~a(~a+c)b~a~ab+~acb~a~ab+~acb+~b(~a+c)bIdenpotencia~a~ab~ab~ab+~acb+~b(~a+c)bAbsorcin~ab+~acb~ab~ab+~b(~a+c)bComplemento~b(~a+c)b~ab+0~ab