Shorter logic, same truth

Computing · Computer Systems · ages 16-17

Name ______________________ Date ____________

Which expression equals not (A and B)?
- (not A) and (not B)
- (not A) or (not B)
- A or B
p and q is True in exactly which case?
- both p and q are true
- at least one is true
- both are false
In not A or B, the NOT applies to A alone before the OR runs.
Circle one: True False
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
With x True and y False, what is not (x and y)?
- False
- it cannot be decided
- True
A long form needs 4 gates and its simplified form needs 1. How many gates are saved?
Answer: ______________
Two forms agree on every truth table row, and the short one uses two fewer gates. What does the saving buy?
- less silicon and less delay with identical answers
- different answers on edge cases
- freedom to skip testing
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

Answer key

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

(not A) or (not B) · De Morgan flips each side and swaps AND for OR.
both p and q are true · AND returns True only when its two sides are both true.
True · NOT binds tightest, so it grabs A first and OR comes last.
A true, B false · There the true form gives True while the friend form gives False, so they differ.
True · x and y is False, and NOT flips it to True.
3 · Subtract to count the saving: 4 minus 1 leaves 3 gates spared.
less silicon and less delay with identical answers · Fewer gates cost less and answer faster, while the checked table keeps meaning identical.
(not late) or (not unpaid) · Unless both faults hold means not (late and unpaid), which De Morgan turns into the OR of the flips.