$6.$ Using the K$-$map to simplify the following functions

a$.$ F$($a$,$b$,$c$)=$ m$(1,5,6,7)$

b$.$ F$($a$,$b$,$c$)=$ m$(0,1,2,3,4,5)$

c$.$ F$($a$,$b$,$c$,$d$)=$ m$(0,2,5,7,8,10,13,15)$

d$.$ F$($a$,$b$,$c$,$d$)=$ m$(1,4,5,6,8,9,11,13,15)$

e$.$ F$($a$,$b$,$c$,$d$,$e$)=$ m$(1,3,8,9,11,12,14,17,19,20,22,24,25,27)$