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 ?
To find the most appropriate combination of P, Q, and R, we analyze which numbers fall into specific regions of the Venn diagram represented by the rectangle, triangle, and ellipse.
The numbers associated with each shape are:
- Rectangle: 1
- Triangle: 2
- Ellipse: 3
The regions in the Venn diagram are as follows:
- P: Inside the ellipse only
- Q: Inside both triangle and ellipse
- R: Inside both rectangle and triangle, but outside the ellipse
Now, let us determine the numbers for P, Q, and R:
- P: The number that is in the overlap of the triangle and ellipse is 6. Therefore, P = 6.
- Q: The only number inside the triangle and the ellipse (but not exclusively in either) is 5. So, Q = 5.
- R: The number in the overlap of the rectangle and triangle (but outside the ellipse) is 3. Hence, R = 3.
After placing these numbers into their respective positions:
| Shape | Region | Number |
|---|---|---|
| Ellipse | P | 6 |
| Triangle & Ellipse | Q | 5 |
| Rectangle & Triangle | R | 3 |
The correct combination is:
P = 6; Q = 5; R = 3
Therefore, the most appropriate answer is the option: P = 6; Q = 5; R = 3.
Important Questions from Logical Deduction
- The following observation is made about the scores obtained by 100 students in an exam:
'For each student, there exists another student in the class such that their scores are at most ten marks away.'
If the above statement is false, which one of the following statements is necessarily true? - Consider the following two phonological rules:
Rule 1: Vowel Epenthesis of [ɪ] after sibilant-ending stems
Rule 2: Progressive Voicing Assimilation of the plural affix
Which ONE of the following rule ordering relations apply in the case of regular English pluralization as in ‘horse’ – ‘horses’? Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
- Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
- Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
- The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______
- 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. Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:
$P < Q$
$S > P > T$
$R < T$
If integers 1 through 5 are used to construct such a number, the value of P is:
