Five soldiers A.B.C.D and E volunteer to perform an important an military task i

Question

Five soldiers A.B.C.D and E volunteer to perform an important an military task if their following conditions are satisfied (a).either A or B or both must go (B).either C or E but not both must go. (C).either both A and C go or neither goes. (D).If D goes, then E must also go. (E).If B goes, then A and C must also go. Determine the variables A, B, C, D, and E.so that an unpriced variable will mean that the corresponding soldier has been selected to go. Determine the expression which specifies the combinations of volunteers who can get the assignment.

Explanation / Answer

Begin at case (1) implies A goes

  implies B goes

  implies Both A And B goes

Let us suppose that A goes,If A goes implies C also goes(case(3)) implies E wil not go as C is already going((case(2)) implies No conclusion from (case(4) and (case(5)) implies it gives us AC

Let us suppose that B goes,If B goes then implies C also goes(case(3)) implies AC must  goes(case(5)) implies E will not go as C is already going((case(2)) implies No conclusion from (case(4)) implies (case(3)) only tells that AC will be going implies it gives us AC

Let us suppose that both A and B goes implies AB is going implies C also goes(case(3)) . AC must  goes(case(5)) implies E will not go as C is already going((case(2))implies No conclusion from (case(4) implies(case(3) only tells that AC will be going implies it gives us ACimplies C thus all total ABC is going.

Equation simplifies to AC+AC+ABCAC+AC+ABC=AC+ABC=AC(1+AB)=AC

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