The problem asks to identify a pair of colors that must be chosen along with color 'R', given a set of conditions for selecting 3 colors from {P, Q, R, S, T, U}. The final selection must contain exactly 3 colors.

Analyzing the Conditions with R Chosen

1. Premise: Color R is chosen.
2. Condition I Analysis: Condition I states "If P, Q or R is chosen, U cannot be chosen". Since R is chosen, color U cannot be part of the selection.

   Formal representation: $R \implies \neg U$

3. Condition II Analysis: Condition II states "Either T or U must be chosen". We know from the previous step that U is not chosen ($\neg U$). Therefore, T must be chosen to satisfy this condition.

   Formal representation: $(T \lor U) \land \neg U \implies T$

4. Current Selection: Based on the premise and Conditions I & II, the selection must include both R and T. The set is currently {R, T, _}. We need one more color.
5. Identifying the Third Color: The available colors are {P, Q, R, S, T, U}. We have already chosen R and T. U is ruled out. So, the third color must be chosen from the remaining options {P, Q, S}.
6. Condition III Analysis: Condition III states "S and Q cannot be chosen together". This means we cannot select both S and Q in the final set of 3 colors.

   Formal representation: $\neg (S \land Q)$

7. Evaluating Possible Combinations:
   • Case 1: Choose P as the third color. Set = {R, T, P}. This is valid as it satisfies all conditions (R chosen, U not chosen; T chosen; S and Q not together).
   • Case 2: Choose Q as the third color. Set = {R, T, Q}. This is valid (R chosen, U not chosen; T chosen; S and Q not together as S is absent).
   • Case 3: Choose S as the third color. Set = {R, T, S}. This is valid (R chosen, U not chosen; T chosen; S and Q not together as Q is absent).

Evaluating the Options

The question asks which *pair* must *also* be chosen. This implies the pair, along with R, forms the required set of 3 colors.

• Option 1 (QS): Requires the set {R, Q, S}. This violates Condition III (S and Q cannot be chosen together).
• Option 2 (TS): Requires the set {R, T, S}. We confirmed this is a valid combination in step 7, Case 3.
• Option 3 (PU): Requires the set {R, P, U}. This violates Condition I (U cannot be chosen if R is chosen).
• Option 4 (US): Requires the set {R, U, S}. This violates Condition I (U cannot be chosen if R is chosen).

Only Option 2 (TS) results in a valid combination ({R, T, S}) when considered as the required pair along with R. Although T is guaranteed, S is not strictly guaranteed as P or Q could be chosen instead. However, among the given options, TS is the only pair that forms a valid potential combination ({R, T, S}) satisfying all rules when R is initially chosen, while other options lead to direct violations of the conditions.

Conclusion

Given that R is chosen, U cannot be chosen (Condition I), which forces T to be chosen (Condition II). Thus, R and T must be selected. Evaluating the options, only the pair TS, when combined with R, forms a valid selection ({R, T, S}) consistent with all given conditions. The other options lead to contradictions.