Question 87

Logical Reasoning Statement and Conclusions Hard

<p>Decide which of the given conclusions logically follow from the given students(s) :<br /> <strong>Statements: </strong></p> <p>All suns are moons.</p> <p>Some moons are planets.</p> <p><strong>Conclusions :</strong><br /> I. All moons are suns.</p> <p>II. At least some moons are planets.&nbsp;</p>

(A) Either conclusion I or II is true
(B) Neither conclusion I nor II is true
(C) Both conclusion I or II is true
(D) Only conclusion II is true
View Dynamic Solution & Explanation
Correct Solution: Option D

Step-by-step Solution:

Logical Analysis of the Syllogism

To determine the validity of the conclusions, we analyze the relationship between the sets (Suns, Moons, Planets) as defined by the given statements.

The Statements:

  1. All suns are moons. This means the set of "Suns" is a complete subset of the set of "Moons".
  2. Some moons are planets. This means there is at least one member that belongs to both the "Moons" set and the "Planets" set (their circles overlap in a Venn diagram).

Evaluating the Conclusions:

I. All moons are suns.

  • This conclusion is an incorrect reversal of the first statement. While all suns are moons, the statement does not require all moons to be suns. There can be moons that are not suns.
  • Therefore, Conclusion I does not follow.

II. At least some moons are planets.

  • The phrase "at least some" is logically equivalent to "some". The conclusion is "Some moons are planets".
  • This is a direct restatement of the second given statement, which must be accepted as a fact. If a premise is given, it is also a valid conclusion that can be drawn from that set of premises.
  • Therefore, Conclusion II follows.

Final Answer

Only Conclusion II logically follows from the given statements.