Logical Reasoning - Logical Deduction - Discussion
In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.
- (A) If only conclusion I follows
- (B) If only conclusion II follows
- (C) If either I or II follows
- (D) If neither I nor II follows and
- (E) If both I and II follow.
Statements: Some books are tables. Some tables are mirrors.
- Some mirrors are books.
- No book is mirror.
A is correct.
The only way C can be correct is if a mirror could be anything other than a book, but that would've required further information in the question (which was not given). The instructions and setup we are given means we think of all our choices not as a Venn diagram, but as a box (or a circle, triangle, whatever other shape you like). Now think of some of those books as tables (a smaller box encased within the outer box). Then think of some of those tables as mirrors (an even smaller box inside the inner box). You can't possibly have a mirror that's not also a book in this layout, given this setup. Again, that would have required different information and instructions.
So, given this, only D can be correct.
To apply either or case three conditions have to be fulfilled,
1. One conclusion should be positive and one negative.
2. Both the conclusions should be individually wrong.
3. The elements in both conclusion should be same.
Like in above case through Venn diagram, First condition one is positive and 2 is negative
Second condition both are wrong, Third condition is not fulfilled as in 1 conclusion element is mirror and book but in second conclusion it is book and mirror. As a result third condition is not fulfilled. So, we cannot apply option C.
So, the answer is D only.
1. Some doctors are fools 2. Some fools are rich.
Ans both options contain the extreme terms for this question too, but in the solution, it's been said that there's no definite conclusion.
Whereas for the question (1. Some books are tables. ), it's been said that either 1 or 2 follows. Why?
Can someone kindly explain this?
Some books are tables. Some tables are mirrors.
Taking the 1st statement, it can be deduced that some books are tables. Therefore all tables are books.
Similarly, in the 2nd statement, it can be deduced that some tables are mirrors. Therefore, all mirrors are tables.
The choices given are: some mirrors are books; no book is mirror. Both of these conclusions cannot be drawn and hence D is the answer.
Can someone please explain why am I wrong?
From the given premise two extremes can be drawn:
Some books are mirrors.
No book is mirror.
But in the question it is given 'some mirror are books' which is NOT a converse of 'some book are mirror'.