Stretch tasks Truth Tables and Logic

Round 1: Quiz Blitz

1. Only when both A and B are true AND is true only when everything is true.
2. Only when both A and B are false OR is false only when everything is false.
3. 8 2 x 2 x 2 = 8 combinations.
4. 0 NOT flips whatever it is given.
5. True OR is true when at least one input is true, and that includes both.
6. 0 B OR C is 1, but A is 0, so the AND gives 0.
7. 1 A AND B is 0, then 0 OR 1 is 1. Brackets change the answer.
8. NOT A AND NOT B Both must be false, so both NOTs must be true.
9. A OR (M AND NOT L) With the alarm sounding the door must unlock, whatever else is true.
10. 0, 1, 0, 1 ... changing every row Last column alternates, middle in pairs, first in fours.
11. AND; NOT The three are AND, OR and NOT.
12. It prevents errors, and each correct column can earn a mark Do not evaluate a combined expression in your head.

Round 2: Quick Fire

1. • Each input can only be 0 or 1
   • 2 x 2 x 2 = 8 combinations, one row each
   Model answer

   Each input can only be 0 or 1, so there are two values for each. With three inputs that gives 2 x 2 x 2 = 8 combinations, and the table needs one row for every combination.

2. • The brackets are evaluated first, changing the order
   • With A = 0, B = 0, C = 1, one gives 0 and the other gives 1
   Model answer

   The brackets are evaluated first, so they change the order of the operations. With A = 0, B = 0 and C = 1, A AND (B OR C) gives 0, because A is 0, but (A AND B) OR C gives 1, because C is 1.

3. • Boolean OR is true when both inputs are true too
   • Everyday 'or' often means one or the other but not both
   Model answer

   In Boolean logic, OR is true when at least one input is true, including when both are true. In everyday English, 'or' often means one or the other but not both, as in tea or coffee.

4. • and is evaluated before or, so is_supervised alone lets anyone in
   • Add brackets around the or
   Model answer

   and is evaluated before or, so the condition reads as (age >= 13 and has_consent) or is_supervised. A supervised child under 13 is let in, because is_supervised on its own makes the whole condition true. Adding brackets fixes it: age >= 13 and (has_consent or is_supervised).

Round 3: Big Think

1. • Work out the rows: 2 x 2 x 2 = 8
   • So every combination appears exactly once
   • The last input column alternates 0, 1
   • The middle column goes in pairs and the first in fours
   • Add a working column for each bracket
   • So the brackets are evaluated first, not in your head
   • A correct working column can earn its mark even after a slip
   • Check the rows that are easy to rush, such as the last row
   Model answer

   First work out the number of rows: with three inputs there are 2 x 2 x 2 = 8 rows, so a table with any other number is already wrong. Fill the input columns in a fixed pattern: the last column alternates 0, 1, 0, 1, the middle column goes in pairs and the first column in fours. This guarantees every combination appears exactly once. Then add a working column for each bracket, A AND B and NOT C, and fill those in before the final column, so the brackets are evaluated first and nothing is done in your head. A correct working column also earns its mark even if the final column has a slip. Finally, check the rows that are easy to rush, such as the last row, where A AND B is 1 so the output is 1 even though NOT C is 0.

2. • Program conditions are Boolean expressions
   • An example condition with brackets
   • A truth table shows every combination of a condition's inputs
   • So it exposes bugs such as a missing bracket
   • It gives test data for each branch
   • Truth tables are used for logic gates too
   • And for checking real systems such as a fire door
   • A conclusion that the claim is wrong
   Model answer

   The claim is wrong. Every condition in a program, such as an if statement or a while loop, is a Boolean expression, for example age >= 13 AND (has_consent OR is_supervised). A truth table lists every possible combination of the inputs, so it shows exactly when the condition is true, and it exposes bugs such as a missing bracket that lets the wrong users in. It also gives test data: one test for each row checks the code behaves as intended. Truth tables are certainly used for logic gates in circuits, but they are equally useful for checking real systems such as a fire door or a login. Overall, I disagree: they are a tool for any Boolean logic, not just hardware.

This or That

1. 0 AND needs both inputs to be 1.
2. 1 OR needs at least one input to be 1.
3. 4 2 x 2 = 4 combinations.
4. AND age >= 13 AND age <= 65: both conditions must hold.
5. OR Nobody is both under 13 and over 65, so AND would never be true.
6. 0 1 AND 1 is 1, and NOT flips it to 0.
7. 1 NOT B is 1, and 1 AND 1 is 1.
8. The working columns Marks are often given per column, so a correct working column scores even after a slip.

Memory Match

• A 3 AND: True only when every input is true
• B 5 OR: True when at least one input is true
• C 1 NOT: Flips its input
• D 6 Truth table: Every input combination with its output
• E 4 Boolean: A value that is only true or false
• F 2 Logic gate: A component performing one logical operation

Sort It

1. Output 0 0 OR 0 OR is false only when everything is false.
2. Output 0 NOT (1 OR 0) 1 OR 0 is 1, and NOT flips it to 0.
3. Output 1 (1 AND 0) OR 1 1 AND 0 is 0, then 0 OR 1 is 1.
4. Output 1 1 OR 0 At least one input is 1.
5. Output 1 0 OR 1 One input is 1, so OR gives 1.
6. Output 1 1 AND 1 Both inputs are 1, so AND gives 1.
7. Output 0 1 AND (0 OR 0) 0 OR 0 is 0, then 1 AND 0 is 0.
8. Output 0 1 AND 0 AND needs both inputs to be 1.
9. Output 1 NOT 0 NOT flips 0 to 1.
10. Output 1 NOT 0 AND 1 NOT 0 is 1, then 1 AND 1 is 1.
11. Output 0 0 AND 1 One input is 0, so AND gives 0.
12. Output 0 NOT 1 NOT flips 1 to 0.