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Grade 8 · lesson 2 of 4

Group a Boolean Expression

Evaluate an explicitly parenthesized combination of AND, OR and NOT.

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Supplied materials

  • Paper and pencil; an adult may read aloud. No device, account or purchase is needed.

Learn the idea

Boolean inputs have exactly two values, true and false. Parentheses name the group to evaluate first. NOT reverses a Boolean value; AND needs both operands to be true; OR needs at least one true operand. These lessons use actual Boolean values, avoiding the different behavior some languages give other types.

Fictional puzzle rule: may_start = (has_key OR has_pass) AND NOT paused. Evaluate the parenthesized key/pass group, then NOT paused, then the final AND. A pause blocks the start even when a key is available. Without stating the grouping, a written rule can be misunderstood.

  1. Make columns key, pass, paused, key OR pass, NOT paused, and may_start.
  2. Trace (true, false, false).
  3. Trace (false, true, true).
  4. Try (false, false, false) and explain which group blocks it.
Worked example

See the method in action

(true, false, false): true OR false = true; NOT false = true; true AND true = true. (false, true, true): first group true, NOT paused false, result false. (false, false, false): first group false, result false.

Your turn

Check your reasoning

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For key = false, pass = true, paused = false, what is may_start?

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See the answer and explanation

True

The key/pass OR is true, and NOT paused is also true, so their AND is true.

Take it further

Change only paused to true for the check case. Expected may_start: false. The first group stays true but NOT paused becomes false.

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Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.