Determine reduced Boolean equation and the Karnaugh Map?

Illustration: Determine reduced Boolean equation and the Karnaugh Map for the truth table shown below:

With no reduction the Boolean Equation for the above truth table is:

Y = A'B'C' + AB'C' + A'BC' + ABC' + A'B'C

Every minterm corresponds to an instance in the truth table when the output is high and the Karnaugh Map for the above truth table, with the allowed groupings is shown below:

The map shows two groupings that cover every minterm each of these groupings will reduce to one term.

The two terms those are grouped together A'B'C & A'B'C' reduces to A'B' this is because A' and B' are common to both terms.

The four terms A'B'C' & A'BC' & ABC' & AB'C' that is grouped together reduces to C' this is because C' is the only input common to all four terms.
Thus the Boolean equation Y = A'B'C + A'B'C' + A'BC' + ABC' + AB'C' reduces to

Y = A'B' + C'.