Consider the following categorical statements: 1. All kids are God. 2. No God is a Human. 3. Some Humans are Son. 4. All Son are Men. Based on these statements, which of the following conclusions must be logically true?

Difficulty: Medium

Correct Answer: Both conclusions (a) and (b) follow

Explanation:


Introduction / Context:
This question tests syllogistic reasoning with multiple quantified statements such as all, no and some. We are given relationships among four categories: kids, God, Human, Son and Men. From these, we must decide whether each conclusion is a necessary logical consequence. The key is to translate the English statements into set relations and then see what must hold in every valid diagram.


Given Data / Assumptions:

  • All kids are God. So the set of kids is entirely inside the set of God.
  • No God is a Human. So the sets God and Human do not overlap at all.
  • Some Human are Son. So there is at least one individual who is both Human and Son.
  • All Son are Men. So the set Son is inside the set Men.
  • Conclusion (a): Some Son are not God.
  • Conclusion (b): Some Men are Human.


Concept / Approach:
Whenever we see all and no, we should think of subset and disjoint relationships. When we see some, we think of at least one common element. To decide whether a conclusion must follow, we check if there is any possible Venn diagram that satisfies all the statements but violates the conclusion. If such a counter example exists, the conclusion is not necessary. If every possible arrangement that obeys the statements also satisfies the conclusion, then the conclusion follows.


Step-by-Step Solution:
Step 1: From no God is a Human, the sets God and Human are completely disjoint.Step 2: From some Human are Son, we know that at least one individual belongs to both Human and Son.Step 3: Because that individual is a Human and no Human can be God, that individual cannot belong to the set God.Step 4: However, this person is a Son (from some Human are Son), so there exists at least one Son who is not God. This exactly matches conclusion (a): some Son are not God.Step 5: From all Son are Men, the set Son lies entirely inside Men. Therefore, the specific Son who is Human and not God is also a Man.Step 6: Thus we have at least one individual who is both a Man and a Human. This confirms conclusion (b): some Men are Human.Step 7: Both conclusions are therefore necessarily true whenever the original statements hold.


Verification / Alternative check:
Draw five circles: God, Human, Son, Men and Kids.Place the Human circle disjoint from God due to no God is a Human.Place Son fully inside Men due to all Son are Men.Inside the Human circle, mark some overlap with Son to represent some Human are Son. Those overlapping individuals are Son, Human and Men, but cannot be God.Therefore at least one Son is outside God, and at least one Man is also a Human. No configuration that respects the original statements can avoid these facts.


Why Other Options Are Wrong:
Option a says only conclusion (a) follows, which ignores the clear fact that some Men are Human must also hold.Option b says only conclusion (b) follows, but we have proved that conclusion (a) is equally forced.Option d, neither follows, is directly contradicted by our diagram based reasoning.Option e suggests uncertainty about which conclusion follows, but in reality both follow absolutely from the premises.


Common Pitfalls:
Assuming that if all Son are Men then Son and Men are the same set, which is not necessary.Forgetting that some Human are Son automatically ensures at least one Son is Human, which is banned from the God set.Misreading no God is a Human as no Human is a God and then misplacing the sets, although in this case both readings describe the same disjoint relationship.


Final Answer:
The only option consistent with the logic is that Both conclusions (a) and (b) follow from the given statements.

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