Geometry

Question Analysis:
This question involves applying the Law of Syllogism and the Law of Detachment to draw a valid conclusion from the given statements.
The main focus is on understanding the logical relationships between the statements and identifying which conclusion must be true.

Key Concept Explanation:
Law of Syllogism:
If "If P, then Q" and "If Q, then R" are both true, then "If P, then R" is also true.
Law of Detachment:
If "If P, then Q" is true, and P is true, then Q must be true.

Step-by-Step Solution:
Apply the Law of Syllogism:
From Statement 1 and Statement 2, we can conclude:
"If a number is prime, then it is not divisible by any number other than 1 and itself."
This is because "If P, then Q" and "If Q, then R" together imply "If P, then R."

Apply the Law of Detachment:
Since 11 is prime (P is true), and we have "If P, then R," we can conclude:
"11 is not divisible by any number other than 1 and itself."

Evaluate the Options:
A) 11 has exactly two factors and is not divisible by any number other than 1 and itself.
This is true based on the conclusion above.
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