DLC :

Question

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

a). $ADE$                                                b). $BD(C + E)$

c). $AC$                                                  d). $ABCD'E'$

Answer 1

Start from case (i)$\Rightarrow$A goes

                          $\Rightarrow$B goes  

                          $\Rightarrow$Both A And B goes

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 $AC+AC+ABC$=$AC+ABC=AC\left ( 1+AB \right )=AC$

Comments

Why c is not correct,?It follows all constraints?

Answer 2

I am getting ACE' as the answer, as if we have AC then it implies E' also so should be writen as ACE'