What is a syllogism?

A syllogism is a logical argument with two premises followed by a conclusion that must logically follow.

Statements:

1. All engineers are logical.

2. Some logical people are creative.

Conclusions:
I. Some engineers are creative.
II. All creative people are logical.

Options:
(A) Only I follows
(B) Only II follows
(C) Both I and II follow
(D) Neither I nor II follows

(D) Neither I nor II follows

The premises don’t establish a direct link between engineers and creativity, so neither conclusion follows.

What are the four standard categorical propositions?

"All A are B," "No A is B," "Some A are B," "Some A are not B."

Statements:

1. All students are readers.

2. Some readers are poets.

Conclusions:

I. Some students are poets.

II. Some poets are readers.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

(B) Only II follows
"Some readers are poets" implies "Some poets are readers" but there's no direct relation between students and poets to confirm I.

What is the difference between "some" and "all"?

"Some" means at least one; "All" means every member of the set.

Statements:

1. Some actors are singers.

2. All singers are dancers.

Conclusions:

I. Some actors are dancers.

II. All dancers are actors.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

 (A) Only I follows

Some actors are dancers” (Conclusion I) follows, because the actors who are singers (some actors) are all dancers.
“All dancers are actors” (Conclusion II) does not follow

What does "No A is B" imply?

Sets A and B have no members in common.

Statements:

1. No apple is a vegetable.

2. All vegetables are plants.

Conclusions:

I. No apple is a plant.

II. Some plants are not apples.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

(B) Only II follows

The statements do not imply apples are not plants. However, it's true that some plants are not apples.

What is a possibility-based conclusion in syllogism?

A conclusion that may be true but is not necessarily true in all cases.

Statements:

1. All teachers are educated.

2. Some educated are rich.

Conclusions:

I. Some teachers are rich.

II. All rich are educated.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

(D) Neither I nor II follows

Neither conclusion is definitely true based on the premises; both are just possibilities.

Can an unstated conclusion be valid?

Only if it logically follows from the premises.

Statements:

1. Some women are managers.

2. All managers are leaders.

Conclusions:

I. Some women are leaders.

II. All women are leaders.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

Answer:

Explanation:

• From "Some women are managers" and "All managers are leaders," it follows that at least some women must be leaders (I).

• However, there's no evidence that all women are leaders (II).

Thus, only conclusion I is valid.

Statements:

1. All pens are tools.

2. Some tools are machines.

Conclusions:

I. All machines are pens.

II. Some machines are tools.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

(B) Only II follows

Statement 2 confirms some machines are tools. No information supports all machines being pens.

Statements:

1. All A are B.

2. Some B are not A.

Conclusions:

I. Some B are A.

II. Some A are not B.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

(A) Only I follows

“All A are B” guarantees some B are A; the second conclusion contradicts the first premise.

Statement: Some books are novels.

Conclusions:

I. No book is a novel.

II. Some books are novels.

Options:

(A) Only I follows

(B) Only II follows

(C) Both I and II follow

(D) Neither I nor II follows

(B) Only II follows

The two are complementary; since the statement is "Some books are novels," conclusion II is true and I is false.