Simplify the following Boolean function F$,$ together with the don't$-$care conditions d$,$ and then express the simplified function in sum$-$of$-$minterms form:

F$($A$,$ B$,$ C$,$ D$)=$ Sigma$(1,5,6,7,12,14,15)$

d$($A$,$ B$,$ C$,$ D$)=$ Sigma$(3,4,9,13,11)$

B $+$ B$\text{'}*$ D

Unknown

A $+$ D

B$+$D