← IGCSE Computer Science Paper 2

Writing a logic expression from a problem statement

Give each condition a letter (A, B, C), turn key words like AND, OR and NOT into gates, and use brackets to group parts so that X matches the wording of the statement.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 33

Understanding Writing a logic expression from a problem statement in IGCSE Computer Science Paper 2

What it does: Each condition gets a letter. 'AND' links A and B, 'OR' links that group to C, and brackets show the grouping. 'OR' links A and B, and the machine must also be running. Brackets make sure A OR B is worked out before AND C. The key word AND means both conditions must be true, so the AND gate is used. The brackets group A and B together because the statement says either of them, and the result is then combined with C using AND. NOT applies only to condition B, as the wording says. NOT (A AND B) would invert the whole AND result instead.

Common mistakes: The statement says door OR window, so the alarm sounds when either is open. The line should use OR: X = A OR B. The alarm needs both conditions to be true, so the key word AND gives an AND gate. The line should be X = A AND B.

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This module's key terms are also in a printable crossword (Modules 562–580) and word search (Modules 539–580).

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Learning

Duo

An alarm X sounds if the door is open (A) AND the system is switched on (B). Which expression is correct?

X = A AND BX = A OR B

Matches

X = A AND B OR C

↓

The brackets are missing, so it is unclear which gate is worked out first. The statement 'A and B together, or C' needs (A AND B) OR C.

Applying

Meanings

Term

X = (A AND B) OR C

Meaning

Give each condition a letter (A, B, C), turn key words like AND, OR and NOT into gates, and use brackets to group parts so that X matches the wording of the statement.

Practice

X = (A OR B) AND NOT C

Testing

Gaps

X = A B

Check Answer

Spots

2A = door, B = window

3X = A AND B

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Quick Questions

1. An alarm X sounds if the door is open (A) AND the system is switched on (B). Which expression is correct?

A. X = A AND B ✓

B. X = A OR B

The key word AND means both conditions must be true, so the AND gate is used.

2. What is the first step when writing an expression from a problem statement?

A. Fill in the output column of the truth table

B. Give each condition an input letter such as A, B or C ✓

Start by assigning a letter to each condition. Then turn the key words into gates.

3. A warning light X comes on if the temperature is too high (A) OR the pressure is too high (B), AND the system is armed (C). Which expression matches?

A. X = A OR (B AND C)

B. X = (A OR B) AND C ✓

The brackets group A and B together because the statement says either of them, and the result is then combined with C using AND.

4. A window alarm X sounds if the window is open (A) AND the key is NOT in the panel (B). Which expression is correct?

A. X = A AND (NOT B) ✓

B. X = NOT (A AND B)

NOT applies only to condition B, as the wording says. NOT (A AND B) would invert the whole AND result instead.

5. A safety lock X is on when the door is closed (A) AND either the seat belt is fastened (B) OR the override is on (C). Which expression is correct?

A. X = A AND (B OR C) ✓

B. X = (A AND B) OR C

B OR C is a grouped condition, so it goes in brackets. Without them, C alone could make X true even if the door is open.

Match the Pairs

X = (A AND B) OR C → The alarm sounds if A and B are both 1, or if C is 1 on its own

X = A AND (NOT B) → X is 1 only when A is 1 and B is 0

The alarm sounds if the door is open (A) AND the system is switched on (B), OR if the panic button is pressed (C) → X = (A AND B) OR C

A warning light comes on if the temperature is high (A) OR the pressure is high (B), AND the machine is running (C) → X = (A OR B) AND C

X = A AND B OR C → The brackets are missing, so it is unclear which gate is worked out first. The statement 'A and B together, or C' needs (A AND B) OR C.

X = (A OR B) AND NOT C → NOT C is used, but the statement says C is true (for example, the machine is running). NOT should only be used when the statement says 'not' or 'is off'.

Key Term

X = (A AND B) OR C

Give each condition a letter (A, B, C), turn key words like AND, OR and NOT into gates, and use brackets to group parts so that X matches the wording of the statement.

Fill in the Blanks

1. # A = door open, B = window open X = A AND B

Hint: Type the gate that matches the key word 'and' in the alarm statement.

2. # Alarm if door (A) OR window (B) is open X = A OR B

Hint: Type the gate that matches the key word in the comment, where either condition is enough.

3. # A = door open, B = window locked # Alarm if door open AND window NOT locked X = A AND NOT B

Hint: Type the gate that reverses condition B, as the statement describes.

4. # A = door, B = window, C = key switch # X on if (door OR window) AND key on X = (A OR B) AND C

Hint: Type the symbol that opens the group so the two linked conditions are worked out first.

5. # A = lid shut, B = guard shut, C = override # Runs if lid AND guard shut, or override X = (A AND B) OR C

Hint: Type the input letter given to the override condition.

Spot the Error

Question 1

A # Alarm: door OR window open

B A = door, B = window

C X = A AND B

Line C — The statement says door OR window, so the alarm sounds when either is open. The line should use OR: X = A OR B.

Question 2

A # Alarm: door open AND on

B A = door open, B = system on

C X = A OR B

Line C — The alarm needs both conditions to be true, so the key word AND gives an AND gate. The line should be X = A AND B.

Question 3

A # A guard shut, B stop pressed

B X = A AND B

C # Runs if shut and not pressed

Line B — The statement says the stop button must NOT be pressed, so B needs a NOT gate. The line should be X = A AND (NOT B).

Question 4

A # On if A or B, and not C

B X = (A AND B) AND NOT C

C # A dark, B motion, C override

Line B — The statement says A or B, so the grouped part needs an OR gate, not AND. The line should be X = (A OR B) AND NOT C.

Question 5

A # Buzzer: A, and B or C

B X = (A AND B) OR C

C # X = 1 when buzzer sounds

Line B — The wording says A is needed, together with B or C. The brackets must group B OR C: X = A AND (B OR C).

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