From a group of five boys, P, Q, R, S, T and three girls X, Y, Z, a team of five have to be selected on the basis of the following criteria. S and T cannot be together. R and S have to be together. S and Z cannot be together. Q cannot be put with P. If S is one of the members, which one of the following teams will be formed?
This question involves selecting a team of five members from a group of boys (P, Q, R, S, T) and girls (X, Y, Z) based on several criteria. We are given that S is a member of the team.
Analyzing Team Selection Constraints with S as a Member
We need to form a team of 5 members. The constraints are:
- S is selected.
- R and S have to be together. Since S is selected, R must also be selected. Team so far: {S, R}. We need 3 more members.
- S and T cannot be together. Since S is selected, T cannot be selected.
- S and Z cannot be together. Since S is selected, Z cannot be selected.
- Q cannot be put with P. This means we cannot have both P and Q in the team.
Based on these rules, the available members for the remaining 3 positions in the team are from the set {P, Q, X, Y}. We must exclude T and Z.
Evaluating Team Options
Let's check the given options against the derived rules:
- Option 1: PSXQY - This team includes both P and Q, violating the rule "Q cannot be put with P".
- Option 2: SRYZQ - This team includes Z, violating the rule "S and Z cannot be together".
- Option 3: TXRYS - This team includes T, violating the rule "S and T cannot be together".
- Option 4: RQSYX - This team includes R, Q, S, Y, and X.
- It contains R and S. (Satisfied)
- It does not contain T or Z. (Satisfied)
- It contains Q but not P, so the rule "Q cannot be put with P" is satisfied.
- The team size is 5. (Satisfied)
Conclusion
The only team that satisfies all the given conditions when S is selected is RQSYX.
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