Directions: Study the following information carefully and answer the question given below.

Six professors — U, V, W, X, Y, and Z — deliver guest lectures on six different subjects — Astronomy, Botany, Geology, History, Psychology, and Zoology — on six different days from Monday to Saturday of the same week, but not necessarily in the same order.
Exactly two persons deliver their lectures between the one who lectures on History and X. Not more than two persons deliver their lectures after X. As many persons deliver their lectures before the one who lectures on History as after the one who lectures on Zoology.
V presents immediately after U, but three slots before the one who lectures on Psychology. The one who lectures on Botany presents three slots before Z, but after U. The one who lectures on Astronomy presents immediately before the one who lectures on Botany. Y does not lecture on Botany and delivers their lecture after the one who lectures on Astronomy. W does not lecture on History.

Which of the following statements is/are not true?

I. U lectures on Botany
II. No one delivers a lecture after X
III. V delivers their lecture before the one who lectures on Zoology

The correct option is Only I.

Step-by-Step Explanation:

We are given six professors — U, V, W, X, Y, and Z — who deliver guest lectures on six different subjects (Astronomy, Botany, Geology, History, Psychology, and Zoology) from Monday to Saturday.

Step 1: Determine the positions of U, V, and Psychology.
- V presents immediately after U.
- V presents three slots before the one who lectures on Psychology.
This gives the relative order: U (Day k), V (Day k + 1), and Psychology (Day k + 4).
If U is on Monday (Day 1), then V is on Tuesday (Day 2), and Psychology is on Friday (Day 5).

Step 2: Determine Astronomy, Botany, and Z.
- Astronomy presents immediately before Botany.
- Botany presents after U and three slots before Z.
Since U is on Monday (Day 1), Astronomy must be on Monday (Day 1) and Botany on Tuesday (Day 2).
Then Z, who presents three slots after Botany (Day 2 + 3 = 5), is on Friday (Day 5, Psychology).

Step 3: Determine X, History, and Zoology.
- Exactly two persons deliver their lectures between History and X.
- Not more than two persons deliver after X.
- The number of persons delivering before History equals the number delivering after Zoology.
Placing X on Saturday (Day 6) means History must be on Wednesday (Day 3), leaving two slots (Thursday and Friday) between them.
With History on Wednesday (2 days before History), Zoology must be on Thursday (Day 4) so that 2 days remain after Zoology (Friday and Saturday).
The remaining subject, Geology, is assigned to Saturday (Day 6).

Step 4: Assign the remaining professors (W and Y).
- W does not lecture on History, so W cannot be on Wednesday.
- Thus, Y lectures on History on Wednesday (Day 3), and W lectures on Zoology on Thursday (Day 4).

Final Schedule Summary:
- Monday: U — Astronomy
- Tuesday: V — Botany
- Wednesday: Y — History
- Thursday: W — Zoology
- Friday: Z — Psychology
- Saturday: X — Geology

Evaluating the Given Statements:
- Statement I: "U lectures on Botany" — False (U lectures on Astronomy).
- Statement II: "No one delivers a lecture after X" — True (X delivers on Saturday, the last day).
- Statement III: "V delivers their lecture before the one who lectures on Zoology" — True (V delivers on Tuesday, which is before Zoology on Thursday).

Therefore, the statement that is not true is Only I.