Using a decoder and external gates, design the combinational circui defined by the following three Boolean functions:

a$)$ F$1=$ x$\text{'}$yz$\text{'}+$ xz

b$)$ F$1=($y$\text{'}+$ x$)$z

c$)$ F$2=$ xy$\text{'}$z$\text{'}+$ x$\text{'}$y

d$)$ F$2=$ y$\text{'}$z$\text{'}+$ x$\text{'}$y $+$ yz$\text{'}$

e$)$ F$3=$ x$\text{'}$y$\text{'}$z$\text{'}+$ xy