___(0-10 pts) Describe what a conditional if-then statement and the different parts of a conditional statement. Give at least 3 examples.
___(0-10 pts) Describe what a counter-example is. Give at least 3 examples.
You are viewing: Which Is A Counterexample For The Conditional Statement
___(0-10 pts) Describe the point, line and plane postulates. Give at least 3 examples of each.
A conditional statement is a statement that it is seen as true or false. An if-then conditional statement is a statement that is formed by both a hypothesis and a conclusion. The hypothesis is always going to begin with IF and the conclusion with THEN.
The most important tool in math that takes place also in the outside world is the counter example.
Counterexample: It is a example that makes a theorem or a statement be false(a statement such as a IF THEN statement)
- You only need one counterexample to prove a statement false with no exceptions, only one.
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When a statement has a IF true then the counterexample can make the THEN statement be false.
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Counterexample are useful in geometry to prove that some theorems are false.
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Geometry involves counterexamples in the way taht mkes IF THEN statements be false and make the converese be also false.
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Counterexample proves some conditional statements o be false and it is used as common sense.
Example: If the sun gets close to earth then the ice will melt.
Counterexample: The sun does not get close to earth, it stays in the same position.
Example 2: If the baseball goes to at least 70 miles per hour then a profesional threw it.
Counterexample: The baseball went flying at 85 miles per hour and the one who threw it was not a profesional but only a strong man, Nadal.
Example 3:If the earth loses all the trees then all animals would die.
Counterexample: Most animals would survive becuase many animals leave underwater and dont need the trees for air.
Example 4: If the triangle has a 9 cm diagonally and 11 cm on the bottom then the side must equal 6
Counterexample: The triangle that has 11 cm in the bottom and 9 cm diagonally the it must have 5 cm on the right.
Point, Line and Plane Postulate
Point Postulate:
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Definition: two lines intersect at exactly one point.
Examples:
As you can see point P id the point were two lines exactly meet and it isn’t more tan one point, it is only one.
In the picture above there are two lines intersecting at exactly one point. Of course we need to use our logic because the lines are too thick.
In the sign above as you can see it is an intersection sign so it automatically is a point.
Plane Postulate:
Definition: through any three non-collinear points there is exactly one plane.
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As you can see in the plane there are three points and if you connect them then you make a plane.
As you can see in the picture above this is a triangle in which it has three non-collinear points which make a plane.
As you can see the pentagon of the United States is a plane but only if you see it from the top. This picture has more than three non-collinear points which makes it a plane as well.
Line Postulate:
Defenition: a line that contains at least two points.
Examples:
As you can see this line or rope has more than one point so it makes it a line.
This is also a line because it has more than two points.
This one is also a line because it has more than one point in it so it makes it a line.
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Category: WHICH
