Question

Statements:
(i) All rats are cats.
(ii) All cats are dogs.
Conclusions:
(i) All rats are dogs.
(ii) Some cats are rats.

A. Only conclusion I is true
B. Only conclusion II is true
C. Both conclusion I and II are true
D. Neither conclusion I nor conclusion II is true

Answer 1

Hint: The problem related to syllogism can be solved by drawing the conclusion step by step from each statement. Conclusion should follow the statements logically.

Complete step-by-step solution:
The following is the Venn diagram of rats, cats and dogs.

Concept of Syllogism: The syllogism is described as one of the forms of logical reasoning in which, through the help of two or more than two given assumptions, a precise outcome is obtained. There are different approaches to solving syllogism, but the most efficient method is the Venn diagram.

From the statement I, we can say that all rats are cats and this can be represented on the Venn diagram as shown in the figure as a circle inscribed in another circle, where the inner circle represents the rats and the outer one represents cats.

The statement II states that all cats are dogs and this can be shown on the Venn diagram as an outer circle which represents the dogs.
From the figure it is clear that all rats are inscribed in a circle of dogs. Hence the conclusion is justified. Now it is also clear from the diagram that all cats are inscribed in a circle of dogs. Therefore, statement II is also correct.

Hence, option (C) is the correct answer that is both conclusion I and II are true.

Note: Make sure to draw the Venn diagram for the problem which will simplify the process to get the answer. The syllogisms are the arguments that are composed of three propositions which are major premise, minor premise and the conclusion.