P looks at Q while Q looks at R. P is married, R is not. The number of pairs of people in which a married person is looking at an unmarried person is
1
Married Unmarried Pairs in Relationships
This problem asks us to determine the number of pairs of people where a married person is looking at an unmarried person, based on the given relationships and marital statuses.
Information Provided in the Question
We are given the following facts about individuals P, Q, and R:
- Person P looks at Person Q.
- Person Q looks at Person R.
- Person P is married.
- Person R is not married, meaning R is unmarried.
Our objective is to count the pairs \((X, Y)\) such that X is married and X is looking at Y, where Y is unmarried.
Marital Status Determination
Based on the provided information, we know the definitive marital statuses for P and R:
- P: Married
- R: Unmarried
The marital status of Person Q is not explicitly stated. To solve the problem completely, we must consider both possibilities for Q's status: whether Q is married or Q is unmarried. The final answer should hold true regardless of Q's status.
Looking Pair Analysis
We need to examine the two specified "looking" relationships to see if they fit the criteria (married person looking at an unmarried person).
P Looks at Q Pair Analysis
- P's status: Married (known)
- Q's status: Unknown
For the pair (P, Q) to be counted, P must be married (which is true) and Q must be unmarried. So, this pair qualifies only if Q is unmarried.
Q Looks at R Pair Analysis
- Q's status: Unknown
- R's status: Unmarried (known)
For the pair (Q, R) to be counted, Q must be married and R must be unmarried (which is true). So, this pair qualifies only if Q is married.
Q's Marital Status Scenarios
Let's evaluate the total number of qualifying pairs under each possible scenario for Q's marital status:
| Scenario for Q | Pair (P looks at Q) | Pair (Q looks at R) | Total Qualifying Pairs |
|---|---|---|---|
| Scenario A: Q is Married |
P (Married) looks at Q (Married) Does NOT qualify (Married looking at Married) |
Q (Married) looks at R (Unmarried) QUALIFIES (Married looking at Unmarried) |
1 |
| Scenario B: Q is Unmarried |
P (Married) looks at Q (Unmarried) QUALIFIES (Married looking at Unmarried) |
Q (Unmarried) looks at R (Unmarried) Does NOT qualify (Unmarried looking at Unmarried) |
1 |
Qualifying Pairs Conclusion
The analysis above clearly shows that regardless of the marital status of Q, the number of pairs where a married person is looking at an unmarried person remains constant.
- If Q is married, the only pair that fits the criteria is (Q looks at R).
- If Q is unmarried, the only pair that fits the criteria is (P looks at Q).
In both logical scenarios, we consistently identify exactly 1 such qualifying pair.
Therefore, the number of pairs of people in which a married person is looking at an unmarried person is 1.
Important Questions from Critical Reasoning
As a responsible person, which of the following is not advisable?
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Given question has main statement followed by four statements. Choose the ordered pair of statements, where the first statement implies the second, and the two statements are logically consistent with the main statement.
When she takes an examination, she clears it.
A. she took an examination
B. she did not take an examination
C. she cleared it.
D. she did not clear it.
You are alone in your house and there is a danger of thieves around. You hear a knock on the door. What should be your most logical action?
While traveling in a train, you notice that a lady from the coach behind you falls from the stairs of the train. What should be your best rational course of action?
