Geometry

Question Analysis
This question involves logical notation and transformations of conditional statements.
The main focus is on understanding the contrapositive statement (~q → ~p) and identifying its correct verbal representation.

Key Concept Explanation:
For a conditional statement p→q:
Contrapositive (¬q → ¬p): This means negating both the hypothesis and conclusion and reversing the order.
Given statement: "If an animal is a bird (p), then it has feathers (q)."
Contrapositive: "If an animal does not have feathers (¬q), then it is not a bird (¬p)."

Step-by-Step Solution:
Identify p and q:
p: The animal is a bird.
q: The animal has feathers.
Negate both p and q:
¬q: The animal does not have feathers.
¬p: The animal is not a bird.
Form the contrapositive:
"If an animal does not have feathers, then it is not a bird."
Match with the given answer choices.

Option Analysis:
A) If an animal is not a bird, then it does not have feathers. → This is the inverse (¬p → ¬q). Incorrect.
B) If an animal does not have feathers, then it is not a bird. → This matches the contrapositive (¬q → ¬p). Correct!
C) If an animal has feathers, then it is a bird. → This is the converse (q → p). Incorrect.
D) An anim...