AP CSP Day 54: Bandwidth Limits
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Practice Question
Consider the Boolean expression:
NOT (p AND q) OR (p AND NOT q)For which combination of p and q does this expression evaluate to false?
When p=true and q=true: NOT(true AND true) OR (true AND NOT true) = NOT(true) OR (true AND false) = false OR false = false. This is the only combination that produces false.
B) p=false, q=true: NOT(false AND true) OR (false AND NOT true) = NOT(false) OR (false AND false) = true OR false = true. C) p=false, q=false: NOT(false AND false) OR (false AND NOT false) = NOT(false) OR (false AND true) = true OR false = true. D) The expression does evaluate to false when both p and q are true.
Students try to simplify the expression algebraically and make errors, or they evaluate NOT(p AND q) without completing the full OR with the second sub-expression.
For complex Boolean expressions, test each answer choice by substituting the values and evaluating step by step. Work inside-out: evaluate innermost expressions first.
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