Statements: Some hens are cows. All cows are horses.
Conclusions:
Some horses are hens.
Some hens are horses.
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
Both I and II follow
Explanation
Since one premise is particular, the conclusion must be particular and should not contain the middle term. So, II follows. I is the converse of II and so it also holds.
Logical Deduction problems
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1. Statements: Some desks are caps. No cap is red.
Since one premise is particular and the other premise is negative, the conclusion must be particular negative and should not contain the middle term. So, it follows that 'Some desks are not red'. However, I is the converse of the first premise and thus it holds.
2. Statements: Raman is always successful. No fool is always successful.
Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, only II follows.
Since both the premises are particular no definite conclusion follows. However, I and II involve only the extreme terms and form a complementary pair. Thus, either I or II follows.
5. Statements: All huts are mansions. All mansions are temples.
As discussed above, it follows that 'All huts are temples'. I is the converse of this conclusion and so it holds. II is the converse of the second premise and so it also holds.
6. Statements: All water is divine. All temples are divine.
Since both the premises are universal and affirmative, the conclusion must be universal affirmative. However, conclusion II, being an A-type proposition, distributes the term 'cats'.
Since the term 'cats' is distributed in II without being distributed in any of the premises, so conclusion II cannot follow. Thus, only I follows.
8. Statements: All young scientists are open-minded. No open-minded men are superstitious.
Since one premise is particular, the conclusion must be particular and should not contain the middle term. Thus, it follows that 'Some pastries are chocolates', I is the converse of the second premise and so it holds. Since both the premises are affirmative, the conclusion cannot be negative. Thus, II does not follow.
10. Statements: All boys are honest. Sachin is honest.
Both the premises are A type propositions. So, the middle term 'honest' forming the predicate in each is not distributed in either. Since the middle term is not distributed even once, no definite conclusion follows.