Question

1. the converse form of the statement would be:

if a figure is not a square, then it does not have four equal sides.
if a figure has four equal sides, then it is a square.
a figure is a square if and only if it has four equal sides
if a figure does not have four equal sides, then it is not a square.

1. part a: which statement is the inverse of:

if today is tuesday, then i have geometry class.
if i have geometry class today, then it is tuesday.
if i do not have geometry class today, then it is not tuesday.
if today is not tuesday, then i do not have geometry class.
i have geometry class if, and only if, today is tuesday.

Explanation:

Question 4

To find the converse of a conditional statement "If \( p \), then \( q \)", we swap the hypothesis (\( p \)) and the conclusion (\( q \)) to get "If \( q \), then \( p \)". Let the original statement (implied, since we're finding its converse) be "If a figure is a square, then it has four equal sides" (where \( p \): "a figure is a square", \( q \): "it has four equal sides"). Swapping \( p \) and \( q \) gives "If a figure has four equal sides, then it is a square".

• The first option is the inverse of the contrapositive (or a wrong negation), the third is a biconditional, and the fourth is the contrapositive. So the correct converse is the second option.

The inverse of a conditional statement "If \( p \), then \( q \)" is formed by negating both the hypothesis (\( p \)) and the conclusion (\( q \)), resulting in "If not \( p \), then not \( q \)". For the statement "If today is Tuesday (\( p \)), then I have Geometry class (\( q \))", the inverse negates \( p \) (today is not Tuesday) and \( q \) (I do not have Geometry class), giving "If today is not Tuesday, then I do not have Geometry class".

• The first option is the converse, the second is the contrapositive, and the fourth is a biconditional. So the correct inverse is the third option.

Answer:

B. If a figure has four equal sides, then it is a square. (Note: Assuming the options are labeled as A, B, C, D with the first option as A, second as B, etc. as per typical multiple-choice formatting.)

Question 5 (Part A)