Instructions

In each of the questions below are given three statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be variance from commonly known facts. Read the conclusion and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Question 41

Statements: Some dogs are rats
All rats are trees
Some trees are not dogs
Conclusions:
I. Some trees are dogs
II. All dogs are trees
III. All rats are dogs
IV. No trees is dogs

Solution

We use elimination to find an exception to the generality of the conclusions. Thus we prove they are not implied. The diagram above satisfies all the statements but contradicts all the conclusions except I. Since we found an exception, the conclusions are not true in "every" case. Thus they are not implied.

We can draw many scenarios that satisfy the statements using Venn diagrams and check for the validity of the conclusions. Conclusion I holds in every case. So, it is implied.