Question

Every Mathematician is a Statistician. Some Statisticians are also Computer Scientists. No Computer Scientist is a Mathematician. Which of the following conclusions necessarily follows?
I. Some Statisticians are not Mathematicians.
II. All Statisticians are Computer Scientists.
III. Some Mathematicians are Computer Scientists
Select the most appropriate option:

• A. Only I
• B. Only II and III
• C. Only I and III
• D. I, II and III

Hint:

For syllogism questions, carefully analyze overlaps and exclusions. Use Venn diagrams to visualize which conclusions logically follow.

Answer 1

The Correct Option is A

Step 1: Analyze statements —
All Mathematicians are Statisticians → Mathematicians ⊆ Statisticians.
Some Statisticians are Computer Scientists.
No Computer Scientist is a Mathematician → Mathematicians ∩ Computer Scientists = ∅.
Step 2: Evaluate conclusions —
I. Some Statisticians are not Mathematicians → True, because some Statisticians are Computer Scientists, who are not Mathematicians.
II. All Statisticians are Computer Scientists → Not necessarily true.
III. Some Mathematicians are Computer Scientists → False, no Mathematician is a Computer Scientist.
Step 3: Conclusion — Only I necessarily follows.