GATE 2022 | Maths | GA Question 3

Question

Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some bottles are cups.
Statement 2: All cups are knives.
Conclusion I: Some bottles are knives.
Conclusion II: Some knives are cups.
Conclusion III: All cups are bottles.
Conclusion IV: All knives are cups.
Which one of the following options can be logically inferred?

 

A) Only conclusion I and conclusion II are correct

(B) Only conclusion II and conclusion III are correct

(C) Only conclusion II and conclusion IV are correct

(D) Only conclusion III and conclusion IV are correct

Answer 1

GATE Electrical 2022 | GA Question: 4

Answer 2

If some bottles are cups and all cups are knives, then some bottles are also knives.
so option A is correct

Answer 3

(C) Only conclusion II and conclusion IV are correct.

Let's analyze the given statements and conclusions:

Statements:

1. Some bottles are cups.
2. All cups are knives.

Conclusions: I. Some bottles are knives. II. Some knives are cups. III. All cups are bottles. IV. All knives are cups.

Analysis:

• Statement 1 tells us that there is an intersection between bottles and cups, but it doesn't specify anything about knives.
• Statement 2 tells us that all cups are knives.

Conclusions: I. Some bottles are knives. (Cannot be logically inferred from the given statements.) II. Some knives are cups. (This can be inferred from the fact that all cups are knives.) III. All cups are bottles. (Cannot be logically inferred. Statement 1 only establishes a one-way relationship from bottles to cups.) IV. All knives are cups. (This can be inferred from statement 2.)