← ACARA Digital Technologies Years 9–10

Tracing a compound condition step by step

Work out each part as TRUE or FALSE for the current values, record both in the trace table, then combine them with AND, OR or NOT. Do brackets first.

Part of: ACARA Digital Technologies Years 9–10 — Algorithms with Logical Operators — Module 45, QCE Digital Solutions Unit 1 — Programmed Solutions — Module 78, QCE Digital Solutions Unit 4 — Prototype Digital Data Exchanges — Module 54, WA Computer Science ATAR Year 11 — Pseudocode and Algorithm Design — Module 64

Understanding Tracing a compound condition step by step in ACARA Digital Technologies Years 9–10

What it does: The columns show each part's result separately (count < 5 and lives > 0), then a final column for the combined result. The bracket (a > 2 AND b < 4) is traced first to get TRUE or FALSE, and only then does NOT reverse that result. OR is TRUE when at least one part is TRUE. hasTicket = TRUE is TRUE, so the whole condition is TRUE.

Common mistakes: 65 is greater than or equal to 50, so part A is TRUE, not FALSE. Each part must be worked out correctly before combining. The trace says NOT raining is TRUE, so raining must be FALSE. The values on line 1 should be temp=30, raining=FALSE.

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This module's key terms are also in a printable crossword (Modules 492–534) and word search (Modules 459–534).

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Learning

Duo

score = 8 and lives = 0. What is the result of: score > 5 AND lives > 0?

TRUE AND FALSE → TRUETRUE AND FALSE → FALSE

Matches

WHILE n < 10 AND found = FALSE Trace: only one column for the whole condition

↓

The trace table records only the final result, so you cannot tell which part made the loop stop. Add a column for n < 10 and a column for found = FALSE.

Applying

Meanings

Term

trace a compound condition

Meaning

Work out each part as TRUE or FALSE for the current values, record both in the trace table, then combine them with AND, OR or NOT. Do brackets first.

Practice

lives ← 5

Testing

Gaps

TRUE AND FALSE is

Check Answer

Spots

1score ← 65

2// A: score >= 50 is FALSE

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Quick Questions

1. score = 8 and lives = 0. What is the result of: score > 5 AND lives > 0?

A. TRUE AND FALSE → TRUE

B. TRUE AND FALSE → FALSE ✓

score > 5 is TRUE but lives > 0 is FALSE. AND is only TRUE when both parts are TRUE, so the whole condition is FALSE.

2. age = 12 and hasTicket = TRUE. What is the result of: age >= 16 OR hasTicket = TRUE?

A. FALSE OR TRUE → TRUE ✓

B. FALSE OR TRUE → FALSE

OR is TRUE when at least one part is TRUE. hasTicket = TRUE is TRUE, so the whole condition is TRUE.

3. You are tracing WHILE x < 10 AND y <> 0. How should you set up the trace table?

A. Add a column for x < 10, a column for y <> 0, and a column for the whole condition ✓

B. Only record the final TRUE or FALSE for the whole condition

Extra columns for each part let you see exactly how the result was worked out, so mistakes are easier to spot.

4. a = 5 and b = 1. How do you trace: NOT (a > 3 OR b > 3)?

A. Apply NOT to a > 3 first, then combine the answer with b > 3 using OR

B. Work out a > 3 OR b > 3 inside the brackets first (TRUE), then apply NOT → FALSE ✓

Brackets are always worked out first. The NOT applies to the result of the whole bracket, not to just one part.

5. a = 2, b = 9, c = 1. What is the result of: (a > 5 OR b > 5) AND c > 5?

A. (FALSE OR TRUE) AND FALSE → TRUE AND FALSE → FALSE ✓

B. (FALSE OR TRUE) AND FALSE → TRUE OR FALSE → TRUE

Do the brackets first: FALSE OR TRUE is TRUE. Then TRUE AND FALSE is FALSE. The AND does not change into an OR.

Match the Pairs

(age >= 13) AND (score > 50) → Work out each bracketed part as TRUE or FALSE first, then combine the two results with AND. Both parts must be TRUE for the whole condition to be TRUE.

x < 3 OR done = TRUE → Check each part separately and record TRUE or FALSE in its own trace table column, then combine with OR. Only one part needs to be TRUE for the whole condition to be TRUE.

Brackets are worked out first, then the NOT or the AND/OR that uses their results → NOT (a > 2 AND b < 4)

WHILE n < 10 AND found = FALSE Trace: only one column for the whole condition → The trace table records only the final result, so you cannot tell which part made the loop stop. Add a column for n < 10 and a column for found = FALSE.

NOT (x > 5 AND y > 5) with x = 8, y = 2: NOT x > 5 = FALSE, so the answer is FALSE → The brackets were not worked out first. The bracket (8 > 5 AND 2 > 5) is TRUE AND FALSE = FALSE, so NOT FALSE = TRUE.

Key Term

trace a compound condition

Work out each part as TRUE or FALSE for the current values, record both in the trace table, then combine them with AND, OR or NOT. Do brackets first.

Fill in the Blanks

1. WHILE score < 50 AND lives > 0 DO score < 50 is TRUE, lives > 0 is FALSE TRUE AND FALSE is FALSE

Hint: Type the final value when both recorded parts are combined with the operator that needs every part to be true.

2. temp ← 35, rain ← 0 temp > 30 is TRUE, rain > 5 is FALSE TRUE OR FALSE is TRUE

Hint: Type the logical operator that gives a true result when only one of the two recorded parts is true.

3. a ← 5, b ← 1, c ← 0 (a > 3 OR b > 3) AND c > 3 (TRUE OR FALSE) AND FALSE: TRUE AND FALSE

Hint: Brackets are worked out first. Type the value the bracketed part becomes.

4. UNTIL found = TRUE OR tries = 3 found = TRUE is FALSE, tries = 3 is TRUE Loop stopped because tries = 3 was TRUE

Hint: Type the variable name from the part of the condition that made the loop stop.

5. IF NOT (n > 5) AND n > 2 THEN n ← 4: n > 5 is FALSE, NOT FALSE is TRUE n > 2 is TRUE, so the whole condition is TRUE

Hint: Type the logical operator that flips a FALSE value into TRUE.

Spot the Error

Question 1

A score ← 65

B // A: score >= 50 is FALSE

C // B: score < 60 is FALSE

D // A AND B is FALSE

Line B — 65 is greater than or equal to 50, so part A is TRUE, not FALSE. Each part must be worked out correctly before combining.

Question 2

A // temp=30, raining=TRUE

B // A: temp > 25 is TRUE

C // B: NOT raining is TRUE

D // A AND B is TRUE

Line A — The trace says NOT raining is TRUE, so raining must be FALSE. The values on line 1 should be temp=30, raining=FALSE.

Question 3

A // A is TRUE, B is FALSE

B // A OR B is TRUE

C // A AND B is TRUE

Line C — AND is only TRUE when both parts are TRUE. B is FALSE, so A AND B is FALSE.

Question 4

A // A=FALSE, B=FALSE, C=TRUE

B // (A OR B) is TRUE

C // (A OR B) AND C is TRUE

Line A — If A and B were both FALSE, (A OR B) would be FALSE. The values should be A=TRUE, B=FALSE, C=TRUE to match the rest of the trace.

Question 5

A // A=FALSE B=TRUE C=FALSE

B // (B AND C) is TRUE

C // A OR (B AND C) is FALSE

Line B — B is TRUE but C is FALSE, so (B AND C) is FALSE. Brackets are worked out first, so this must be correct.

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