Step-by-step Solution:

Quick Solution

This is a classic logic puzzle that can be solved by creating a table and filling it in with the information from the clues. We need to match each of the five roommates to one task and one day of the week.

1. Step-by-Step Deductions

1. Start with the most direct clues:
   • From Clue 2: Sally = Dusting.
   • From Clue 3: The task on Thursday = Mopping.
   • From Clue 4: Terry's day is Wednesday.
   • From Clue 5: The task on Friday = Laundry.
   • From Clue 6: Randy's day is Monday.
2. Deduce the remaining Days:
   • We have assignments for Monday (Randy) and Wednesday (Terry).
   • Clue 2 says Sally does not work on Monday or Friday. Since Wednesday is taken by Terry, Sally's day must be Tuesday.
   • This leaves Thursday and Friday for the remaining two roommates, Uma and Vernon.
3. Assign Uma and Vernon:
   • We know the person working on Thursday does Mopping, and the person on Friday does Laundry.
   • Clue 5 says the Laundry is "not by Uma". So Uma cannot work on Friday.
   • Therefore, Uma works on Thursday and does the Mopping.
   • By elimination, Vernon must work on Friday and do the Laundry.
4. Deduce the final Tasks:
   • The only tasks left are Sweeping and Vacuuming.
   • The only roommates without tasks are Randy and Terry.
   • Clue 4 says Terry's task is "not vacuuming".
   • Therefore, Terry must be doing the Sweeping. (This answers the question).
   • By elimination, Randy's task is Vacuuming.

2. The Final Arrangement

Final Answer: The task Terry does on Wednesday is Sweeping.