Statements: All good athletes win. All good athletes eat well.
Conclusions:
All those who eat well are good athletes.
All those who win eat well.
Options
A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D. Neither I nor II follows
E. Both I and II follow
Correct Answer
Neither I nor II follows
Explanation
Since the middle term 'good athletes' is distributed twice in the premises, the conclusion must be particular and should not contain the middle term. So it follows that 'Some of those who win, eat well'.
Logical Deduction problems
Search Results
1. Statements: All fishes are grey in colour. Some fishes are heavy.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, it follows that 'Some heavy things are grey in colour'. I is a cumulative result of this conclusion and the first premise. Thus, only I holds.
2. Statements: Some swords are sharp. All swords are rusty
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, I follows. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.
3. Statements: No gentleman is poor. All gentlemen are rich.
The first premise is an E-type proposition, So, the middle term 'gentleman' forming the subject is distributed. The second premise is an A-type proposition. So, the middle term 'gentlemen' forming the subject is distributed. Since the middle term is distributed twice, the conclusion cannot be universal. Since one premise is negative, the conclusion must be negative. Thus, it follows that 'Some rich men are not poor'. Thus, neither I nor II follows.
4. Statements: Some dedicated souls are angels. All social workers are angels.
The first premise is an I type proposition. So, the middle term 'angels' forming the predicate is not distributed. The second premise is an A type proposition. So, the middle term 'angels' forming the predicate is not distributed. Since the middle term is not distributed even once in the premises, no definite conclusion follows.
5. Statements: All fish are tortoise. No tortoise is a crocodile.
Since both the premises are universal and one premise is negative, the conclusion must be universal negative. Also, the conclusion should not contain the middle term. So, II follows; I is the converse of II and thus it also holds.
6. Statements: All film stars are playback singers. All film directors are film stars.
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, I follows. II is the converse of the second premise and so it also holds.
7. Statements: All hill stations have a sun-set point. X is a hill station.
Conclusions:
X has a sun-set point.
Places other than hill stations do not have sun-set points.
Since both the premises are universal and affirmative, the conclusion must be universal affirmative and should not contain the middle term. So, only I follows.
8. Statements: Some dreams are nights. Some nights are days.
Since the middle term 'tigers' is not distributed even once in the premises, no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. So, either I or II follows.
10. Statements: All poles are guns. Some boats are not poles.