Exercise 1: Translating (P and Q) or (not P) into Boolean Algebra Notation — Possible Solution
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GIVEN
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Propositional logic statement: (P ^ Q) v ~P
(using ^ for AND, v for OR, ~ for NOT, since this file uses plain
text)

STEP 1: TRANSLATE EACH PIECE USING THIS CHAPTER'S OWN TABLE
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P and Q      -> P, Q become the Boolean variables x, y
P ^ Q (AND)  -> x . y   (or simply xy)
~P (NOT)     -> x'
v (OR)       -> +

STEP 2: ASSEMBLE THE FULL EXPRESSION
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(P ^ Q) v ~P   translates directly to   (x . y) + x'

RESULT
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Boolean algebra form: xy + x'

WHY THIS WORKS AS AN ANSWER
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Each individual piece of the original statement is translated
using exactly this chapter's own correspondence table (AND -> .,
OR -> +, NOT -> '), then reassembled in the same structure as the
original statement, rather than skipping straight to a simplified
or rewritten form - this exercise is specifically about the
notation translation, not simplification (which is Chapter 5's own
job).