GATE CH 2023 | GA | Question: 6

Question

Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement "Some human beings are not cruel creatures" is $\text{FALSE,}$ then which of the following set of statement(s) can be logically inferred with certainty?

1. All human beings are cruel creatures.
2. Some human beings are cruel creatures.
3. Some creatures that are cruel are human beings.
4. No human beings are cruel creatures.

• A. only (i)
• B. only (iii) and (iv)
• C. only (i) and (ii)
• D. (i), (ii) and (iii)

Comments

i did it by drawing some daigrams.

Answer 1

Statement $S1$:$-$ "Some human beings are not cruel creatures" is FALSE, this means either

(1)Some human beings are cruel creature(due to these human beings statement S1 is false) $->$ option (iii) too.
so opt (ii),(iii) are correct.

--or---
(2)what if not some but ALL human beings are cruel creatures
so opt (i) is correct too.


 

Answer 2

we're given that the statement "Some human beings are not cruel creatures" is FALSE.

in logic, if "Some A are not B" is false, it means "All A are B" must be true.

therefore, in this imagined world, "All human beings are cruel creatures" must be true.    .....................(1)

now, let's evaluate each of the given statements:

(i) "All human beings are cruel creatures" - this is directly inferred from our conclusion in (1). so, it's TRUE.

(ii) "Some human beings are cruel creatures" - if all human beings are cruel creatures, then it's also true that some human beings are cruel creatures. so, this is also TRUE.

(iii) "Some creatures that are cruel are human beings" - if all human beings are cruel creatures, then it must be true that at least some cruel creatures are human beings. so, this is again TRUE.

(iv) "No human beings are cruel creatures" - this contradicts our conclusion (1) that all human beings are cruel creatures. so, this is FALSE.

therefore, statements (i), (ii), and (iii) can be logically inferred with certainty.