Software Testing · Quiz 2 · Jan 2026

**1. Identify the key property:** Prime paths are simple paths. Edge-pair coverage also requires consecutive edges involving self-loops, such as m-n-n and n-n-m, which repeat an internal vertex and are not simple. **Answer: C — Because edge-pair coverage requires self-loops to be visited..** A: **Incorrect:** PPC does subsume ordinary edge coverage. B: **Incorrect:** Some self-loop edge pairs are not simple paths. C: **Correct:** It requires self-loop-related edge pairs that PPC can miss. D: **Incorrect:** Universal subsumption fails for graphs with self-loops.

**1. Use the base test:** Start with \((A_2,B_1,w,Z_1)\). **2. Vary one characteristic at a time:** For block counts 4,2,5,3, BCC needs \[1+(4-1)+(2-1)+(5-1)+(3-1)=11.\] **Answer: B — 11.** A: **Incorrect:** The stated structure gives 11, rather than 10. B: **Correct:** This equals the independently counted result 11. C: **Incorrect:** The stated structure gives 11, rather than 12. D: **Incorrect:** The stated structure gives 11, rather than 14.

**1. Compare c values:** For \(p=(a\lor b)\land\neg c\), c=true makes p=false, while c=false makes \(p=a\lor b\). **2. Require a change:** Flipping c changes p exactly when \(a\lor b=true\). Hence \(p_c=a\lor b\). **Answer: D — \(a\lor b\).** A: **Incorrect:** Both a and b false make c inactive. B: **Incorrect:** Negating a is not the required determination condition. C: **Incorrect:** This is incorrect when a=false,b=false, and misses a=false,b=true. D: **Correct:** At least one of a,b true allows c to determine the predicate.

**1. Identify the key property:** Creating and managing assignments and quizzes is a specific capability the system must provide, so it is functional. **Answer: A — Functional requirement.** A: **Correct:** It specifies required application behaviour. B: **Incorrect:** It is a capability rather than a quality constraint. C: **Incorrect:** No regulatory obligation is stated. D: **Incorrect:** It describes detailed system functionality rather than a high-level business objective.

**1. Identify valid price classes:** 0.5–1.4, 1.5–4.9, 5.0–9.9, and 10.0 or higher have four different charges. **2. Add invalid weights:** Values below 0.5 form one additional invalid class. One-decimal rounding removes gaps between the stated valid ranges. Thus there are five classes. **Answer: C — 5.** A: **Incorrect:** The stated structure gives 5, rather than 3. B: **Incorrect:** The stated structure gives 5, rather than 4. C: **Correct:** This equals the independently counted result 5. D: **Incorrect:** The stated structure gives 5, rather than 6.

**1. Identify the key property:** Cyclomatic complexity is the size of a basis of linearly independent control-flow paths. **Answer: D — linearly independent paths.** A: **Incorrect:** Prime paths belong to a different coverage criterion. B: **Incorrect:** The number of loops alone does not determine complexity. C: **Incorrect:** All test paths can be far more numerous or infinite. D: **Correct:** The path-basis size equals cyclomatic complexity.

**1. Identify limits:** For \(-10\le temp\le40\), test immediately below, at, and above each endpoint. **2. Collect boundary neighbourhoods:** \(\{-11,-10,-9\}\) and \(\{39,40,41\}\) together give the maximal set offered. **Answer: B — \(\{-11,-10,-9,39,40,41\}\).** A: **Incorrect:** It misses the just-inside values −9 and 39. B: **Correct:** It covers below/at/above both endpoints. C: **Incorrect:** It only checks the endpoints. D: **Incorrect:** It omits out-of-range values on both sides.

**1. Read the continuation condition:** Each positive input is added. Zero or negative input triggers break. **2. Express n continuing inputs and a stop:** \[PC=\left(\bigwedge_{i=0}^{n-1}r_i>0\right)\land r_n\le0.\] The initial accumulator a does not affect input numbering. **Answer: A — \((\bigwedge_{i=0}^{n-1}r_i>0)\land r_n\le0\).** **Convention note:** The literal while(true) guard never becomes false. The question’s outcomes refer to continuing versus breaking after reading a fresh input. A: **Correct:** It gives n positive inputs followed by a nonpositive input. B: **Incorrect:** Zero cannot continue, and input numbering does not start at a. C: **Incorrect:** This encodes n+1 continuing inputs. D: **Incorrect:** It has incorrect bounds, continuation inequality and exit index.

**1. Read the form:** \((x\land y\land z)\lor(\neg a\land\neg b)\lor(\neg p\land q)\) is a disjunction of conjunctions: DNF. **2. Count independent Boolean inputs:** There are seven distinct variables x,y,z,a,b,p,q, hence \(2^7=128\) valuations. **Answer: A, D — DNF and 2^7 valuations.** A: **Correct:** The top-level connective joins conjunctions by OR. B: **Incorrect:** The displayed expression is not a conjunction of disjunctions. C: **Incorrect:** Three counts conjunction groups rather than seven independent Boolean variables. D: **Correct:** Seven independent variables give 2^7 valuations.

**1. Activate a:** In \(p=\neg c\lor(a\land\neg b)\), a determines p only if c=true and b=false. **2. Choose opposite a values with opposite p outcomes:** Row 3 is (T,F,T), giving p=true. Row 7 is (F,F,T), giving p=false. Both make a active, satisfying CACC. **Answer: A — (3,7).** A: **Correct:** Both rows make a active and switch both a and p. B: **Incorrect:** Row 8 has c=false, which masks a and makes p=true. C: **Incorrect:** Row 6 has b=true,c=false and masks a. D: **Incorrect:** Neither pair member makes a active under the required b,c setting.

**1. Make c inactive:** For \(p=\neg c\lor(a\land\neg b)\), a=true,b=false force p=true regardless of c. **2. Hold a,b fixed:** Rows 3 and 4 differ only in c and both keep p=true. An inactive c cannot keep p=false because setting c=false always makes p=true. **Answer: B — (3,4) for p=true; no pair for p=false.** A: **Incorrect:** Rows 2 and 4 change b rather than c. B: **Correct:** Rows 3 and 4 change only c and keep p=true. C: **Incorrect:** Rows 1 and 3 change b and do not keep p unchanged. D: **Incorrect:** Rows 1 and 4 change more than c.

**1. Count the connected graph:** \(N=6\), \(E=7\). **2. Calculate:** \(V=E-N+2=7-6+2=3\). **Answer: C — 3.** A: **Incorrect:** The stated structure gives 3, rather than 5. B: **Incorrect:** The stated structure gives 3, rather than 6. C: **Correct:** This equals the independently counted result 3. D: **Incorrect:** The stated structure gives 3, rather than 4.

**1. Enumerate length-two paths:** 1-2-3, 1-2-6, 2-3-4, 3-4-5, 4-5-4, 4-5-6, 5-4-5. **2. Count each distinct adjacent-edge combination:** These are seven edge-pair requirements. **Answer: B — 7.** A: **Incorrect:** The stated structure gives 7, rather than 8. B: **Correct:** This equals the independently counted result 7. C: **Incorrect:** The stated structure gives 7, rather than 9. D: **Incorrect:** The stated structure gives 7, rather than 10.

**1. Supply two covering paths:** 1-2-6 covers the early exit; 1-2-3-4-5-4-5-6 covers the longer branch and both loop directions. **2. Prove minimality:** Once an execution takes 2→6 it terminates, so no single path can cover that edge and 2→3. Two paths are necessary and sufficient. **Answer: B — 2.** A: **Incorrect:** The stated structure gives 2, rather than 3. B: **Correct:** This equals the independently counted result 2. C: **Incorrect:** The stated structure gives 2, rather than 1. D: **Incorrect:** The stated structure gives 2, rather than 4.

**1. Locate definitions:** x is defined at node 1 and redefined at node 4. **2. Cover each definition:** Both have reachable print(x) uses, so each requires at least one definition-clear use path: two obligations. **Answer: B — 2.** A: **Incorrect:** The stated structure gives 2, rather than 1. B: **Correct:** This equals the independently counted result 2. C: **Incorrect:** The stated structure gives 2, rather than 3. D: **Incorrect:** The stated structure gives 2, rather than 4.

**1. Enumerate distinct def-clear paths:** From definition 1, the paths are 1-2 (predicate use), 1-5 (predicate and print use), and 1-2-5 (print use). **2. Include the second definition:** Definition 4 has path 4-5 to print(x). There are four distinct graph-path sequences; 1-2-3-4-5 cannot carry the original x through its redefinition. **Answer: B — 4.** A: **Incorrect:** The stated structure gives 4, rather than 5. B: **Correct:** This equals the independently counted result 4. C: **Incorrect:** The stated structure gives 4, rather than 3. D: **Incorrect:** The stated structure gives 4, rather than 2.

**1. Symbolically execute assignments:** \(t_1=y_0^3\) and \(t_2=3x_0z_0\). **2. Conjoin the two taken branches:** Abort requires the outer \(x_0>z_0\) and inner \(t_1-t_2<0\), giving \[x_0>z_0\land(y_0^3-3x_0z_0<0).\] **Answer: C — \(x_0>z_0\land y_0^3-3x_0z_0<0\).** A: **Incorrect:** The nonstrict outer comparison includes inputs that do not enter the branch. B: **Incorrect:** A positive difference does not execute abort. C: **Correct:** Both strict branch conditions match the code. D: **Incorrect:** Both nonstrict comparisons admit equality cases not reaching abort.

**1. Evaluate the initial run:** At (5,2,3), x>z and \(2^3-3(5)(3)=8-45=-37<0\), so abort occurs. **2. Flip the target inner branch:** Keep \(x_0>z_0\), but negate the strict inner test to \(\ge0\). Thus the next constraint is \[x_0>z_0\land(y_0^3-3x_0z_0\ge0).\] **Answer: B — \(x_0>z_0\land y_0^3-3x_0z_0\ge0\).** A: **Incorrect:** It reverses the preceding outer branch instead of the target inner branch. B: **Correct:** It preserves the prefix and includes equality in the negated inner test. C: **Incorrect:** It does not correctly flip the inner branch and changes the outer condition. D: **Incorrect:** Negating <0 gives ≥0, not >0.

**1. Identify three path classes:** Outer false; outer true with inner true (abort); outer true with inner false. **2. Evaluate B’s triples:** (5,2,3) aborts because 8−45<0; (4,8,2) enters the outer branch without abort because 512−24>0; (5,8,10) skips the outer branch. **3. Compare candidates:** B includes a representative of every class. **Answer: B — {(5,2,3),(4,8,2),(5,8,10)}.** A: **Incorrect:** It omits the outer-false class. B: **Correct:** All three feasible execution classes are represented. C: **Incorrect:** The first triple has x=z and does not abort, so the abort class is missing. D: **Incorrect:** All three inputs enter the outer branch, so its false outcome is missing.