Introduction to Logic and Euclidean Geometry — Test
Question 9 • Geometry
Read the statement. Doubling the dimensions of a rectangle increases the area by a factor of 4 If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4 , which are true? Choose two correct answers.
Answer
A
q rightarrow p represents the original conditional statement.
B
p rightarrow approximates q represents the contrapositive of the original conditional statement.
C
approximates p rightarrow approximates q represents the inverse of the original conditional statement.
D
p rightarrow q represents the original conditional statement.
E
approximates q rightarrow approximates p represents the converse of the original conditional statement.
Explanation
The original conditional is p → q: doubling the rectangle’s dimensions (p) leads to its area increasing by a factor of 4 (q). Choice D states that original conditional. The inverse switches both statements to their negations, giving not-p → not-q, which is choice C. The contrapositive would be not-q → not-p, so choice B is not correct.
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