6. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?

  1. ABCDEF
  2. AB
  3. AB + CD + EF
  4. A + B + C + D + E + F
  5. A + B(C+D(E+F))

2 is CORRECT. Repeated application of the absorption theorem x + xy = x on pairs of terms in the expression gives the desired result. For example:

AB + ABC       + ABCD      +  ABCDE      + ABCDEF
--------
AB + ABC  = AB                                        (x = AB, y = C)
            ---------
            AB + ABCD = AB                            (x = AB, y = CD)
                        ---------
                        AB + ABCDE = AB               (x = AB, y = CDE)
                                     -----------
                                     AB + ABCDEF = AB (x = AB, y = CDEF)

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