Question

In the following question below are given some statements followed by some conclusions. Taking the given statements to be true even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusion logically follows the given statements.

Statements:
1. No pens are pencils.
2. No eraser is cup.
3. All pencils are erasers.
Conclusions:
I. Some pencils are not erasers.
II. Some erasers are not pens.
III. No pencil is cup.
IV. Some erasers are cups.

• A. Only conclusion (I) and (IV) follow
• B. Only conclusion (I) and (III) follow
• C. Only conclusion (II) and (III) follow
• D. Only conclusion (II) and (IV) follow

Answer 1

Answer:

C. Only conclusion (II) and (III) follow

• Let's analyze the statements and conclusions using a Venn diagram approach:

• Statement 1: No pens are pencils. This means the "pens" and "pencils" circles are completely separate.

• Statement 2: No eraser is cup. This means the "erasers" and "cups" circles are completely separate.

• Statement 3: All pencils are erasers. This means the "pencils" circle is entirely inside the "erasers" circle.

• Now, let's evaluate the conclusions:

• Conclusion I: Some pencils are not erasers. This is false. Statement 3 says all pencils are erasers.

• Conclusion II: Some erasers are not pens. This is true. Since all pencils are erasers, and no pencils are pens, some erasers (specifically, those that are pencils) are not pens.

• Conclusion III: No pencil is cup. This is true. We know all pencils are erasers, and no eraser is a cup. So no pencils are cups.

• Conclusion IV: Some erasers are cups. This is false. Statement 2 says no eraser is a cup.

• Therefore, the conclusions that logically follow the given statements are:

• II. Some erasers are not pens.

• III. No pencil is cup.