Understanding the Persons and Cars Logic Puzzle

This is a logic puzzle where six persons (G, H, R, T, U, V) each like one unique car from a set of six cars (C1, C2, C3, C4, C5, C6). We are given several clues about who likes which car or which cars they do not like. Our goal is to determine a possible pair of cars liked by U and V, respectively.

Analyzing the Given Clues

Let's list the information we have:

• T likes C3. (T → C3)
• V does not like C1 or C2.
• G does not like C1 or C2.
• R likes either C6 or C2. (R → C6 or R → C2)
• H does not like C5.
• U likes either C2 or C6. (U → C2 or U → C6)
• Each person likes a different car.

From the first clue, we know T is assigned to C3. This car is now taken.

From the clues about R and U, they must like either C2 or C6. Since each car is unique, one of them likes C2 and the other likes C6. There are two possibilities for the R/U pair:

1. R likes C6 and U likes C2. (R → C6, U → C2)
2. R likes C2 and U likes C6. (R → C2, U → C6)

Exploring Possibilities for U and V

Let's examine the constraints and see which pairs for U and V are possible based on the options provided.

We know:

• U must like C2 or C6.
• V must not like C1 or C2.
• T likes C3.

So far, cars C2, C3, and C6 are involved with T, R, and U. Cars C1, C4, C5 remain, along with persons G, H, V.

Consider the options for the pair (U, V):

Option 1: (U, V) = (C2, C5)

• Assume U likes C2 and V likes C5.
• Given U likes C2, R must like C6 (as R likes C2 or C6, and C2 is taken by U). So, R → C6.
• Current assignments: U → C2, V → C5, T → C3, R → C6.
• Remaining persons: G, H.
• Remaining cars: C1, C4.
• Let's check the constraints for G and H:
  • G does not like C1 or C2. U likes C2, so G doesn't like C1. G must like C4. (G → C4)
  • H does not like C5. V likes C5. H must like C1. (H → C1)
• Proposed full assignment: G → C4, H → C1, R → C6, T → C3, U → C2, V → C5.

Let's verify all original clues with this full assignment:

• T likes C3: Yes.
• V doesn’t like C1 and C2: V likes C5. Yes.
• G doesn’t like C1 and C2: G likes C4. Yes.
• R likes either C6 or C2: R likes C6. Yes.
• H doesn’t like C5: H likes C1. Yes.
• U likes either C2 or C6: U likes C2. Yes.
• All persons like different cars: C4, C1, C6, C3, C2, C5 - all unique. Yes.

Since this assignment satisfies all conditions, the pair (U, V) = (C2, C5) is possible.

Option 2: (U, V) = (C6, C1)

• Assume U likes C6 and V likes C1.
• Constraint for V: V does not like C1. This option violates this constraint directly.

So, (C6, C1) is not a possible pair for (U, V).

Option 3: (U, V) = (C3, C4)

• Assume U likes C3 and V likes C4.
• Constraint for T: T likes C3. U cannot like C3 as cars must be unique. This option violates the uniqueness and T's constraint.

So, (C3, C4) is not a possible pair for (U, V).

Option 4: (U, V) = (C1, C5)

• Assume U likes C1 and V likes C5.
• Constraint for U: U likes either C2 or C6. U cannot like C1. This option violates U's constraint.

So, (C1, C5) is not a possible pair for (U, V).

Conclusion

By checking each option against the given constraints and possible assignments, only the pair (U, V) = (C2, C5) satisfies all the conditions simultaneously, allowing for a complete and valid assignment of cars to all persons.