Simplify the following boolean expressions to minimum number of literals:

a$.($A $+$ B$)($A $+$ B$)($A$+$ C$)$

b$.$ A$$B$$C $+($A$+$B$+$C$)+$ A$$B$$C$$D

c$.$ XY $+$ X$($Y$+$Z$)+$ Y $($Y$+$Z$)$

d$.($AB$($C$+$BD$)+$A$$B$)$C