Exercise 2: Tracing OR(0,1) Built Entirely From NAND — Possible Solution
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GIVEN
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x=0, y=1. Compute OR(x,y) using only:
  NOT(a) = NAND(a,a)
  OR(x,y) = NAND(NOT(x), NOT(y))

STEP 1: COMPUTE NOT(x) = NAND(x,x)
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NOT(0) = NAND(0,0)

NAND(0,0): AND(0,0)=0, so NAND(0,0) = NOT(0) = 1 (using the base
NAND truth table directly here, since this is the primitive
operation everything else is built from)

NOT(x) = 1

STEP 2: COMPUTE NOT(y) = NAND(y,y)
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NOT(1) = NAND(1,1)

NAND(1,1): AND(1,1)=1, so NAND(1,1) = NOT(1) = 0

NOT(y) = 0

STEP 3: COMPUTE OR(x,y) = NAND(NOT(x), NOT(y)) = NAND(1, 0)
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NAND(1,0): AND(1,0) = 0, so NAND(1,0) = NOT(0) = 1

OR(x,y) = 1

RESULT
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OR(0,1) = 1, computed using only NAND operations at every step.
This matches the actual truth table value for OR(0,1), which is 1
(since at least one input is 1).

WHY THIS WORKS AS AN ANSWER
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Every single operation in the chain is expanded down to a raw NAND
application (not skipped or shortcut using the "actual" OR/NOT
truth tables), showing concretely how this chapter's own
functional-completeness claim plays out for one specific real
input pair.