Five soldiers A, B, C, D and E volunteer to perform an important military task if their following conditions are satisfied
(i) either A or B or both must go
(ii) either C or E but both must not go
(iii) either both A and C go or neither goes
(iv) If ‘D’ goes, then ‘E ’ must also go
(v) If ‘B’ goes, then A and C must also go
The minimal combination of soldiers who can get the arrangement will be

Let A goes,If A goes $\Rightarrow$C also goes(case(iii)) $\Rightarrow$E wil not go as C is already going((case(ii))$\Rightarrow$No conclusion from (case(iv) and (case(v)) $\Rightarrow$it gives us AC

Let B goes,If B goes then $\Rightarrow$C also goes(case(iii))$\Rightarrow$ AC must goes(case(v)) $\Rightarrow$E will not go as C is already going((case(ii))$\Rightarrow$No conclusion from (case(iv)$\Rightarrow$(case(iii) only tells that AC will be going$\Rightarrow$it gives us AC

Let Both A and B goes$\Rightarrow$AB is going $\Rightarrow$C also goes(case(iii)) $$AC must goes(case(v)) $\Rightarrow$E will not go as C is already going((case(ii))$\Rightarrow$No conclusion from (case(iv)$\Rightarrow$(case(iii) only tells that AC will be going$\Rightarrow$it gives us AC $\Rightarrow$Cthus all total ABC is going.

Our equation simplifies to $AC+AC+ABC$=$AC+ABC=AC\left ( 1+AB \right )=AC$