Question

3. All philosophers are lovers of truth. No lovers of truth are closed-minded people. Thus no philosophers are closed-minded people. Invalid 8. Some politicians are idealistic persons. No idealistic persons are scientists. So some scientists are not politicians. 11. No A are B. All C are A. So, no Care B 12. All A are B. ALL A are C. So, some Care B. 21. All M are P. No S are M. So, no S are P.

Answer 1

3.

If we consider set theory to solve the question;

Set for philosophers (P) is a subset of set for lovers of truth(L)

L and set for closed minded people(C) are mutually exclusive sets

Hence P and C should also be mutually exclusive sets.

i.e. no philosophers are closed-minded people

Answer: TRUE/VALID

8.

If we consider set theory to solve the question;

Set for politicians (P) and set for idealistic persons (I) are overlapping sets

I and set for scientists (S) are mutually exclusive sets

But the statement in question some scientists are not politicians may not be true in the case when S is the subset of P and not mutually exclusive to I.

Answer: FALSE/INVALID

11.

If we consider set theory to solve the question;

A and B are mutually exclusive sets

C is a subset of A

Hence C and B have to be mutually exclusive sets

Answer: TRUE/VALID

12.

If we consider set theory to solve the question;

A is a subset of B

A is a subset of C

Hence B and C have to be overlapping sets with at least the set A in common

i.e. Some C are B

Answer: TRUE/VALID

13.

If we consider set theory to solve the question;

M is a subset of P

S and M are mutually exclusive sets

But the statement in question no S are P may not be true in the case when S and P are overlapping sets while S and M being mutually exclusive.

Answer: FALSE/INVALID