Introduction:
In this question, we are given a set of liquids and we need to identify which set comprises liquids that are poor conductors of electricity. Let's analyze each set of liquids to determine their electrical conductivity.

Set A: shampoo, vegetable oil, distilled water
- Shampoo: Shampoo is mainly composed of water, surfactants, and various conditioning agents. These ingredients do not possess free ions that can conduct electricity. Therefore, shampoo is a poor conductor of electricity.
- Vegetable oil: Vegetable oil is a nonpolar substance and does not contain free ions. As a result, it does not conduct electricity effectively and is considered a poor conductor.
- Distilled water: Distilled water is pure water that has been stripped of impurities, including ions. Since it lacks ions, it does not conduct electricity well and is classified as a poor conductor.

Set B: sugar solution, vinegar, lemon juice
- Sugar solution: Sugar, when dissolved in water, forms a solution that does not contain free ions. As a result, it does not conduct electricity effectively and is considered a poor conductor.
- Vinegar: Vinegar is primarily composed of acetic acid, which is a weak electrolyte. It dissociates partially into ions in solution, allowing it to conduct electricity to some extent. Therefore, vinegar is not a poor conductor.
- Lemon juice: Lemon juice contains citric acid, which is also a weak electrolyte. Similar to vinegar, it can conduct electricity to some extent due to the presence of ions. Therefore, lemon juice is not a poor conductor.

Set C: tap water, shampoo, honey
- Tap water: Tap water may contain dissolved minerals and ions, making it a good conductor of electricity. Therefore, tap water is not a poor conductor.
- Shampoo: As discussed earlier, shampoo is a poor conductor of electricity due to the absence of free ions.
- Honey: Honey is a viscous liquid composed primarily of sugars. Like sugar solutions, it does not contain free ions and is therefore a poor conductor of electricity.

Set D: salt solution, lemon juice, vinegar
- Salt solution: Salt solutions, such as sodium chloride dissolved in water, are excellent conductors of electricity. The dissolved salts dissociate into ions, allowing the solution to conduct electricity effectively. Therefore, salt solution is not a poor conductor.
- Lemon juice and vinegar have already been discussed in Set B and are not poor conductors.

Conclusion:
After analyzing each set of liquids, we find that Set A (shampoo, vegetable oil, distilled water) comprises liquids that are poor conductors of electricity. Shampoo, vegetable oil, and distilled water do not contain free ions and therefore do not conduct electricity effectively.