Simplify the following logical expressions algebraically

a$)f(u,x,v,y,z)=y*z+u*y+(y+z)*(u+y)+(x+v+z)*(x+u+v)*(x+v+z)*(x+u+v)$

b$)f(a,b,c,d,e)=b*c*d+a*b*c*e+a*d+b*c*e+b*c*d$

c$)f(a,b,c,d)=(b+c)*(c+d)+a*c+b*c+(c+a)*(c+b)$