GATE2017 EC-1: GA-5

Question

Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences?

1. At least one bench is a table
2. At least one shelf is a bench
3. At least one chair is a table
4. All benches are chairs

• A. Only i   
• B. Only ii
• C. Only ii and iii
• D. Only iv

Comments

option 2?

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@himgta

yes option 2 is correct..

Answer 1

Possible Venn diagram based on the given facts :-

Now, according to above Venn diagram,

1. At least one bench is a table -- False
2. At least one chair is a table -- False
3. All benches are chairs -- False

Since, some shelves are chairs  and all chairs are benches, at least one shelf must be a bench.

So, option (B) is correct.  

Comments

@chirudeepnamini Make any venn diagram and then check options one by one and then think how to make option incorrect and then do modification in the venn diagram.

For example, suppose, you have created the 2nd venn diagram. Now, take option i) atleast one bench is a table. Now, think, "can this statement be wrong ?" , Now, think, what is the possibilty. Now, you will think about your 1st and 3rd venn diagram which will still satify the given facts.  

Similarly for 3rd option.

Now, for 4th option, think, is it possible to make this option wrong and all facts still be satisfied. Then you will switch from your 1st venn diagram to 3rd venn diagram.

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@ankitgupta.1729 thanks for reply and it  is a good method..

I have thought of a method based on your method :

1--we draw all possible venn diagrams.

2--we say that a option can be concluded from the given statements in the question,only if it is true in all possible venn diagrams ...

If it is wrong in even in 1 venn diagram, we can eliminate that option...

Is this method correct??

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@chirudeepnamini of course, it is correct :)