Question $1$: $[10$ marks: $2$ mark each$]($Easy$,$ Warm Up$)$Explain five of the following terms in two or three sentences.a$.$ Distributivityb. Dualityc. Dont Care Conditiond. Latch versus Flip$-$Flope. Sequential Logic $($Circuit$)$ vs$.$ Combinational Logic $($Circuit$)$f$.$ Clockg. Level vs$.$ Edge$-$triggered Memory CellQuestion $2$: $[10$ marks$]($Easy$)$Simplify F$=(1,3,5,7,8)+$ d$(10,12,13,14,15)$ in the form of product of sums $($PoS$)$ using $4-$variable K$-$map.Question $3$: $[10$ marks$]($Moderate$)$Simplify F$=(1,3,5,7,8)+$ d$(10,12,13,14,15)$ algebraically.Question $4$: $[5$ marks: $2\mathrm{.}5$ marks each$]($Easy but Tricky$)$In a binary multiplier that multiplies an n$-$bit $($first number$)$ by m$-$bit $($second number$)$ binary numbers,a$.$ How many k$-$bit adders are needed?b$.$ How many bits would be in the output including the last carry?Question $5$: $[10$ marks$]($Moderate$)$Design F $=(1,2,5,7,8,10,15)$ using $8-$to$-1$ MUX.