Writing a logic expression from a problem statement

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Date:

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Quick Questions

Shade in the A or B circle for each question.

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

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

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

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)

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

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1X = (A AND B) OR C		AThe 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.
2X = A AND (NOT B)		BX = (A OR B) AND C
3The alarm sounds if the door is open (A) AND the system is switched on (B), OR if the panic button is pressed (C)		CThe alarm sounds if A and B are both 1, or if C is 1 on its own
4A warning light comes on if the temperature is high (A) OR the pressure is high (B), AND the machine is running (C)		DNOT 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'.
5X = A AND B OR C		EX is 1 only when A is 1 and B is 0
6X = (A OR B) AND NOT C		FX = (A AND B) OR C

Definitions

X = (A AND B) OR C

Fill in the Blanks

Complete each line of code by filling in the missing parts.

# A = door open, B = window open X = A ___ B

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

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

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

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

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A # Alarm: door OR window open

B A = door, B = window

C X = A AND B

Question 2

A # Alarm: door open AND on

B A = door open, B = system on

C X = A OR B

Question 3

A # A guard shut, B stop pressed

B X = A AND B

C # Runs if shut and not pressed

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

Question 5

A # Buzzer: A, and B or C

B X = (A AND B) OR C

C # X = 1 when buzzer sounds

Answer Key

Writing a logic expression from a problem statement

Section A: Quick Questions

A — X = A AND B

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

B — X = (A OR B) AND C

A — X = A AND (NOT B)

A — X = A AND (B OR C)

Section B: 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'.

Section C: Definitions

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.

Section D: Fill in the Blanks

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

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

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

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

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

Section E: Spot the Error

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

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.

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).

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.

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).