Logical Reasoning - Logical Deduction - Discussion
In each of the questions below are given three statements followed by three conclusions numbered I, II and III, You have to take the given statements to be true even if they seem to be at variance from the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some towels are brushes. No brush is soap. All soaps are rats.
Conclusions:
- Some rats are brushes.
- No rat is brush.
- Some towels are soaps.
Some towels are brushes. No brush is soap.
Since one premise is particular and the other negative, the conclusion must be particular negative (O-type) and should not contain the middle term. So, it follows that 'Some towels are not soaps'. No brush is soap. All soaps are rats.
Since the middle term is distributed twice, the conclusion must be particular. Since one premise is negative, the conclusion must be negative. So, it follows that 'Some brushes are not rats'. Since I and II involve the same terms and form a complementary pair, so either I or II follows.
I think 1 and 3 follow.
Could you please clarify my doubt?
No brush is a soap, all soaps are rats. Assume there are 10B, 15S and 20 R, none of the 10 B are S. Whereas all 15S are R but the remaining Rats can be anything. There is no statement stopping rest of the rats from being brushes (5R!= Soaps).
3 is following in only 1 out of 2 cases.
Some rats may be brushes or no rat is the brush.
And some towels may be soap.
I think only II follows.