A)F= ¬(A ∨ ¬B) → C b) F=¬(A ∧ ¬B ∧ ¬C) c)F=Xv¬(Yv¬(X&Y)) d)F=(XvZ)&(Xv¬Z)&¬X e)F=(¬B→¬A)...

Question

A)F= ¬(A ∨ ¬B) → C b) F=¬(A ∧ ¬B ∧ ¬C) c)F=Xv¬(Yv¬(X&Y)) d)F=(XvZ)&(Xv¬Z)&¬X e)F=(¬B→¬A) &¬(AVB) &(A→C) f)F=(A&B&C)V(¬A&B&C) g) F=(AV¬BVC)& ¬ (AVBVC)

Answer 1

A)F= ¬(A ∨ ¬B) → C = (¬A ^ B) → C = ¬(¬A ^ B) v C =(A v ¬B) v C= A v ¬B v C

b) F=¬(A ∧ ¬B ∧ ¬C)= ¬A v B v C  

c)F=Xv¬(Yv¬(X&Y)) = X v ¬Y ^ (X ^ Y)  

d)F=(XvZ)&(Xv¬Z)&¬X= (XvZ)&(X^¬Xv¬X^¬Z)=(XvZ)&(0v¬X^¬Z)=(XvZ)&(¬X^¬Z)=(X^¬X^¬ZvZ^¬X^¬Z)=(0^¬Zv0^¬X)=0

e)F=(¬B→¬A)&¬(AVB)&(A→C)=(Bv¬A)^¬A^¬B^(¬AvC)=(B^¬Bv¬A^¬B)^(¬A^¬Av¬A^C)=(0v¬A^¬B)^(¬Av¬A^C)=(¬A^¬B)^¬A=¬A^¬B    

f)F=(A^B^C)V(¬A^B^C)=(A^¬A^B^C)v(B^¬A^B^C)v(C^¬A^B^C)=(0^B^C)v(¬A^B^C)v(¬A^B^C)=(¬A^B^C)v(¬A^B^C)=¬A^B^C

g) F=(Av¬BvC)&¬(AvBvC)=(Av¬BvC)^¬A^¬B^¬C=(A^¬A^¬B^¬C v ¬B^¬A^¬B^¬C v C^¬A^¬B^¬C)=(0 v ¬A^¬B^¬C v 0)= ¬A^¬B^¬C