Exercise 1: Tracing the Majority Circuit for x=0, y=1, z=1 — Possible Solution
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GIVEN
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This chapter's own 5-gate majority circuit: A1=AND(x,y),
A2=AND(x,z), A3=AND(y,z), O1=OR(A1,A2), OUT=OR(O1,A3)
Inputs: x=0, y=1, z=1

STEP-BY-STEP GATE TRACE
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A1 = AND(x=0, y=1) = 0
A2 = AND(x=0, z=1) = 0
A3 = AND(y=1, z=1) = 1
O1 = OR(A1=0, A2=0) = 0
OUT = OR(O1=0, A3=1) = 1

RESULT
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Circuit output: 1

CONFIRMING AGAINST majority(0,1,1)
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majority(x,y,z) is 1 when at least 2 of the 3 inputs are 1. Here,
y=1 and z=1 (two of the three inputs are 1), so majority(0,1,1)=1.

Circuit output (1) matches majority(0,1,1) (1). Confirmed.

WHY THIS WORKS AS AN ANSWER
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Every gate in the circuit is traced individually in the order
signals actually flow through it (the three AND gates first, then
the two OR gates), rather than jumping straight to the final
answer, and the result is checked against the actual majority
function definition rather than just assumed correct.