Boolean Algebra and Simplifying Logic Expressions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Shorter logic, same truth

Computing · Computer Systems · ages 16-17
Name ______________________   Date ____________

  1. Which expression equals not (rain and wind)?

    • (not rain) and (not wind)
    • (not rain) or (not wind)
    • rain or wind

  2. p and q is True in exactly which case?

    • both p and q are true
    • at least one of p and q is true
    • both p and q are false

  3. In not X and Y, the NOT applies to X alone before the AND runs.

    Circle one:   True   False

  4. A friend claims not (A and B) equals (not A) and (not B). Which truth table row exposes the mistake?

    • A true, B true
    • A false, B false
    • A true, B false

  5. With x True and y False, what is not (x and y)?

    • False
    • it cannot be decided
    • True

  6. (A and B) or (A and C) or (A and D) simplifies to A and (B or C or D). Counting each two-input AND or OR as one gate, how many gates are saved?

    Answer: ______________

  7. Two forms agree on every truth table row, and the short one uses two fewer gates. What does the saving buy?

    • less silicon and energy, same answers
    • different answers on rare edge-case inputs
    • permission to skip the truth table check

  8. The rule is members enter unless they are both late and unpaid. Which expression matches it?

    • (not late) or (not unpaid)
    • (not late) and (not unpaid)
    • not late and unpaid
LightMySky · lightmysky.comW1-mt_9MrE1N63D5-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Shorter logic, same truth W1-mt_9MrE1N63D5-s1

  1. (not rain) or (not wind) · De Morgan flips each side and swaps AND for OR.
  2. both p and q are true · AND returns True only when both sides are true.
  3. True · NOT runs before AND, so the expression means (not X) and Y.
  4. A true, B false · On that row the true form gives True while the friend's form gives False.
  5. True · x and y is False, and NOT flips it to True.
  6. 2 · The long form uses 3 ANDs and 2 ORs, which is 5 gates. The short form uses 2 ORs and 1 AND, which is 3. 5 minus 3 is 2.
  7. less silicon and energy, same answers · Fewer gates use less silicon and energy, while the matching table keeps the answers the same.
  8. (not late) or (not unpaid) · Unless both faults hold means not (late and unpaid), which De Morgan turns into the OR of the flipped sides.
Worksheet · LightMySky