Is the following function satisfiable xy y zx z Consider

Is the following function satisfiable? ( x+y )(y + z)(x +z ) ?

Consider a school with four classes and two time slots during which the courses can be scheduled.The classes are named A, B, C, and D. The following pairs of courses can not be scheduled at thesame time: (B, C), (A, D), (C, D), (B, A). Express the scheduling problem as a boolean expression.That is, give a boolean expression that is true if and only if there is a feasible schedule for thecourses that satisfies all the constraints.

Solution

( x+y )(y + z)(x +z )

here we have 3 clauses , for this expression to be satisfiable all the 3 clauses need to be satisfiable.

x represents 1 so x(bar) will represent 0

likewise y is 1 and y(bar) is 0

z is 1 and z(bar) is 0

+ represent union or OR operator and all the 3 clauses are in intersection or AND operator

so ( x+y )(y + z)(x +z )

is ( 1+1 )(0 + 0)(0 +1 )

=> (1 OR 1)AND(0 OR 0)AND(0 OR 1)

=> (1)AND(0)AND(1)

=> (0)AND(1)

=> 0 or false

hence the function is not satisfiable