CONDITIONAL STATEMENTS

If-Then Form

100

Ninth graders are in Geometry.

"If you are a ninth grader, then you are in Geometry."

200

Puppies are small.

"If it is a puppy, then it is small"

300

A line contains at least 2 points.

"If it is a line, then it contains at least 2 points."

400

2x is larger than x whenever x is positive.

"If x is positive, then 2x is larger than x."

500

You cannot fly unless you have wings

"(Only) If you have wings, you can fly" or "If you don't have wings, you cannot fly"

Counter-Example

100

If x squared = 9, then x = -3.

"If x squared = 9, then x = 3"

200

All flags have green parts on them.

The American flag does not have green on it.

300

If the area of a swimming pool is 60 square meters, then its sides are 10 meters and 6 meters.

Its sides could be 12 meters and 5 meters.

400

A polygon can have only two right angles.

A square has four right angles.

500

All prime numbers are odd.

2 is a prime number.

Converse

100

If a child is 5 years old, then they are in kindergarten.

"If a child is in kindergarten, then they are 5 years old"

200

If there is snow on the ground, flowers are not in bloom.

"If flowers are not in bloom, then there is snow on the ground."

300

If 2 lines intersect, then they cross each other.

"If 2 lines cross each other, then they intersect."

400

If it is snowing, then it is cold. Is the converse of this statement true or false, and why?

"If it is cold, then it is snowing." FALSE - it can be cold without snowing

500

If two planes intersect, then they intersect in a segment

"If two planes intersect in a segment, they intersect"

Contrapositive

100

If you like Basketball, then you play on the Basketball team.

"If you do not play on the Basketball team, then you do not like Basketball"

200

If x is odd, then 2x is even.

"If 2x is not even, then x is not odd."

300

If a point lies on 2 lines, then it is at the intersection.

"If a point is not at the intersection, then it does not lie on 2 lines."

400

If you like yellow, then you love SpongeBob.

"If you do not love SpongeBob, then you do not like yellow."

500

Triangles don't have more than one right angle

"If a figure have more than one right angle, then is not a triangle"

Inverse

100

If x is odd, then 3x is odd.

"If x is not odd, then 3x is not odd"

200

If you like hockey, then you will go to the hockey game.

"If you do not like hockey, then you will not go to the hockey game."

300

If you visited Ciudad Perdida, then you've been to Santa Marta

"If you have not visited Ciudad Perdida, then you have not been to Santa Marta"

400

If you are 18, then you can legally vote. Is the inverse of this statement true or false, and why?

"If you are not 18, then you can not legally vote." FALSE - those older than 18 (20 years old) can also legally vote

500

If a number is irrational, then it is real.

"If a number is not irrational, then is not real".