AP CSP Day 24: Boolean Logic
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Truth tables systematically show every possible combination of input values and the resulting output for Boolean expressions. Mastering De Morgan's laws helps simplify complex Boolean conditions: NOT (A AND B) is equivalent to (NOT A) OR (NOT B). AP CSP review questions on Boolean logic often combine AND, OR, and NOT in nested expressions where students must apply operator precedence carefully. Short-circuit evaluation, where AND stops early if the first operand is false, is a subtle but testable concept.
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Boolean Logic Review: Complex Expressions
De Morgan's Laws
NOT (A AND B) equals (NOT A) OR (NOT B). NOT (A OR B) equals (NOT A) AND (NOT B). These laws let you rewrite Boolean expressions in equivalent forms. They are especially useful for simplifying or checking complex conditions.
Operator Precedence
NOT applies first (highest precedence), then AND, then OR. So NOT A OR B AND C is evaluated as (NOT A) OR (B AND C). Using parentheses always overrides precedence and makes intent explicit.
NOT A OR B is (NOT A) OR B, not NOT (A OR B).Practice Question
For which of the following values of x does the expression (x > 5) AND (x < 10) evaluate to true?For AND to be true, both conditions must be true simultaneously. When x = 7: 7 > 5 is true AND 7 < 10 is true. Both conditions are satisfied, so the expression is true.
A) x = 3: 3 > 5 is false. Since AND requires both to be true, the expression is false. C) x = 10: 10 < 10 is false (strict inequality). B) x = 5: 5 > 5 is false (strict inequality, not ≥).
Students include boundary values like 5 and 10, confusing strict inequalities (> and <) with non-strict ones (≥ and ≤). The boundary values are excluded with strict operators.
Pay close attention to > versus ≥ and < versus ≤. Boundary values are the most common source of errors on inequality questions.
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