Four students (A, B, C, D) are assigned to four projects (P1, P2, P3, P4), one each.
- A does not get P1.
- B gets P2 or P3.
- C does not get P3.
- D gets P4.
- Step 1: Apply conditions. D gets P4. B gets P2 or P3. A does not get P1. C does not get P3.
- Step 2: Assign D. D = P4. Remaining: P1, P2, P3 for A, B, C.
- Step 3: Assign B. B gets P2 or P3.
- Step 4: Assign others. A not P1, so A gets P2 or P3. C not P3, so C gets P1 or P2.
Try B = P2: A, C get P1, P3. C not P3, so C = P1, A = P3.
Arrangement: C (P1), B (P2), A (P3), D (P4).
Valid. Try B = P3: A, C get P1, P2. C = P1, A = P2 (A not P1). Valid.
- Step 5: Check question. B gets P2 or P3. Options suggest one answer.
From arrangement, B = P2 is consistent.
- Step 6: Check options. Options: (1) P1, (2) P2, (3) P3, (4) P4. P2 matches option (2).
- Step 7: Conclusion. Option (2) is correct.
How many triangles are there in the figure given below?
Disregard commonly known facts. Which conclusion would follow on the basis of given statements only?
Statement (I): Some bottles are car. Some cars are cycle.
Conclusion: \[\begin{array}{rl} \bullet & \text{[(I)] Some bottles are cycle is a possibility.} \\ \bullet & \text{[(II)] All bottles are cycle.} \\ \end{array}\]