Car Collection Logic Puzzle Analysis
The problem involves determining the number of cars owned by S based on three statements, given that only one statement is true.
Let $n$ represent the number of cars S owns.
The statements can be represented mathematically:
- P states: $n \ge 3$
- Q states: $n < 3$
- R states: $n \ge 1$
We are told exactly one of these statements is true.
Evaluating Possible Number of Cars
We test different values for $n$ to see when exactly one statement holds true:
- Case 1: $n=0$
- P ($0 \ge 3$): False
- Q ($0 < 3$): True
- R ($0 \ge 1$): False
- Case 2: $n=1$
- P ($1 \ge 3$): False
- Q ($1 < 3$): True
- R ($1 \ge 1$): True
- Case 3: $n=2$
- P ($2 \ge 3$): False
- Q ($2 < 3$): True
- R ($2 \ge 1$): True
- Case 4: $n \ge 3$
- P ($n \ge 3$): True
- Q ($n < 3$): False
- R ($n \ge 1$): True (since $n \ge 3$ implies $n \ge 1$)
Conclusion
The only scenario where exactly one person (Q) tells the truth is when $n=0$. Therefore, S has 0 cars.
Important Questions from Logical Deduction
- Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of P, Q, and R ?
- Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.
Column-I Column-II P. This house is in a mess. 1. Alright, I won't bring it up during our conversations. Q. I am not happy with the marks given to me. 2. Well, you can easily look it up. R. Politics is a subject I avoid talking about. 3. No problem, let me clear it up for you. S. I don't know what this word means. 4. Don't worry, I will take it up with your teacher.
Identify the option that has the correct match between Column-I and Column-II. - In the following truth table, what does X stand for?
P Q X 1 1 1 1 0 0 0 1 0 0 0 1 A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K).
Which one of the following options displays the color codes that are consistent with the color model?
