Question

1. match the statements to their correct symbols. 20 points.

• converse
• conditional statement
• inverse
• contrapositive

p→q
~q→~p
~p→~q
q→p

1. 10 points

if a quadrilateral has congruent diagonals, then it is a rectangle. what is the inverse of this conditional statement?
a) if a quadrilateral is not a rectangle, then it does not have congruent diagonals.
b) if a quadrilateral does not have congruent diagonals, then it is not a rectangle.
c) if a quadrilateral is a rectangle, then it has congruent diagonals.
d) if a quadrilateral is not a rectangle, then it has congruent diagonals.

1. what is the contrapositive of the statement on question 2? select from the same a,b,c and d from question 2. 10 points

Explanation:

Step1: Recall logic statement forms

A conditional statement is $p
ightarrow q$. The converse is $q
ightarrow p$, the inverse is $\sim p
ightarrow\sim q$, and the contra - positive is $\sim q
ightarrow\sim p$.

Step2: Answer question 1

Converse: $q
ightarrow p$; Conditional Statement: $p
ightarrow q$; Inverse: $\sim p
ightarrow\sim q$; Contrapositive: $\sim q
ightarrow\sim p$

Step3: Answer question 2

The original conditional statement is "If a quadrilateral has congruent diagonals, then it is a rectangle". Let $p$ be "a quadrilateral has congruent diagonals" and $q$ be "it is a rectangle". The inverse is $\sim p
ightarrow\sim q$, which is "If a quadrilateral does not have congruent diagonals, then it is not a rectangle". So the answer is B.

Step4: Answer question 3

The contra - positive of the original statement "If a quadrilateral has congruent diagonals, then it is a rectangle" ($p
ightarrow q$) is $\sim q
ightarrow\sim p$, which is "If a quadrilateral is not a rectangle, then it does not have congruent diagonals". So the answer is A.

Answer:

1. Converse: $q

ightarrow p$; Conditional Statement: $p
ightarrow q$; Inverse: $\sim p
ightarrow\sim q$; Contrapositive: $\sim q
ightarrow\sim p$

1. B. If a quadrilateral does not have congruent diagonals, then it is not a rectangle.
2. A. If a quadrilateral is not a rectangle, then it does not have congruent diagonals.