Choose the correct expression for the given below DAG.
Choose the correct expression for the given below DAG.
Answer: C. a +a*(b-c)+(b-c)*d — Final expression: a + a*(b-c) + (b-c)*d Explanation: Compute the subexpression (b - c) once; the DAG reuses this value rather than recomputing it. Form a*(b -…
- A.
(a*(b-c))+ (a*(b-c))+(b-c)*d
- B.
(a+a)*(b-c)+(b-c)*d
- C.
a +a*(b-c)+(b-c)*d
- D.
None of these
Attempted by 401 students.
Show answer & explanation
Correct answer: C
Final expression: a + a*(b-c) + (b-c)*d
Explanation:
Compute the subexpression (b - c) once; the DAG reuses this value rather than recomputing it.
Form a*(b - c) by multiplying a with the reused (b - c).
Form (b - c)*d by multiplying d with the reused (b - c).
Add the three terms to get the final expression: a + a*(b - c) + (b - c)*d.
Why the other expressions are incorrect:
(a*(b-c))+ (a*(b-c))+(b-c)*d duplicates the product a*(b-c), which contradicts the DAG that uses a and the reused (b-c) without duplicating that multiplication.
(a+a)*(b-c)+(b-c)*d adds a to a before multiplying by (b-c), implying two a terms combined; the DAG instead yields a as a separate term plus a*(b-c), not (a+a).
'None of these' is incorrect because the correct expression appears among the provided choices.