Exercise 1: Verifying (x+y)' Matches the NOR Truth Table — Possible Solution
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GIVEN
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Build NOR(x,y) using only AND, OR, and NOT, as (x + y)'

STEP-BY-STEP FOR EACH INPUT COMBINATION
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x=0, y=0: x+y = 0+0 = 0. (x+y)' = 0' = 1.
x=0, y=1: x+y = 0+1 = 1. (x+y)' = 1' = 0.
x=1, y=0: x+y = 1+0 = 1. (x+y)' = 1' = 0.
x=1, y=1: x+y = 1+1 = 1. (x+y)' = 1' = 0.

RESULT TABLE
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x  y  (x+y)'
0  0  1
0  1  0
1  0  0
1  1  0

COMPARISON TO THIS CHAPTER'S OWN NOR TABLE
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This chapter's NOR table: (0,0)->1, (0,1)->0, (1,0)->0, (1,1)->0

Every row matches exactly.

WHY THIS WORKS AS AN ANSWER
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Each of the 4 input combinations is computed in full (first the OR,
then the NOT applied to that result), and the final table is
compared row by row against this chapter's own stated NOR table
rather than just asserting the identity holds.