Question

directions: for each multiple choice question, circle the correct answer, and write it on the line provided next to each number.

1. which of the following is a conditional statement?

a. all squares are rectangles.
b. if a shape is a square, then it is a rectangle.
c. a shape is a rectangle if it is a square.
d. squares and rectangles are polygons.

1. the conditional statement is: if it is raining, then the ground is wet.

what is the converse?
a. if it is not raining, then the ground is not wet.
b. if the ground is wet, then it is raining.
c. if it is raining, then the ground is wet.
d. if the ground is not wet, then it is not raining.

1. the conditional statement is: if a number is even, then it is divisible by 2.

what is the inverse?
a. if a number is not even, then it is not divisible by 2.
b. if a number is divisible by 2, then it is even.
c. if a number is even, then it is divisible by 2.
d. if a number is not divisible by 2, then it is not even.

1. the conditional statement is: if an angle is a right angle, then it measures 90°.

what is the contrapositive?
a. if an angle does not measure 90°, then it is not a right angle.
b. if an angle measures 90°, then it is a right angle.
c. if an angle is not a right angle, then it does not measure 90°.
d. if an angle measures 90°, then it is not a right angle.

Explanation:

1. A conditional statement has the form "If \(p\), then \(q\)". Option B has this form.
2. The converse of "If \(p\), then \(q\)" is "If \(q\), then \(p\)". So for "If it is raining, then the ground is wet", the converse is "If the ground is wet, then it is raining".
3. The inverse of "If \(p\), then \(q\)" is "If not \(p\), then not \(q\)". For "If a number is even, then it is divisible by 2", the inverse is "If a number is not even, then it is not divisible by 2".
4. The contrapositive of "If \(p\), then \(q\)" is "If not \(q\), then not \(p\)". For "If an angle is a right angle, then it measures \(90^{\circ}\)", the contrapositive is "If an angle does not measure \(90^{\circ}\), then it is not a right angle".

Answer:

1. B. If a shape is a square, then it is a rectangle.
2. B. If the ground is wet, then it is raining.
3. A. If a number is not even, then it is not divisible by 2.
4. A. If an angle does not measure \(90^{\circ}\), then it is not a right angle.