Show:
Vocab
Identify the Hypothesis and Conclusion
Writing a Conditional
Finding a Counterexample
Venn Diagram
100
What is a conditional?
A conditional is another name for an if-then statement.
100
What is the hypothesis and the conclusion of this conditional statement: If Texas won the 2006 Rose Bowl football game, then Texas was college football's 2005 national champion.
Hypothesis: Texas won the 2006 Rose Bowl football game. Conclusion: Texas was college football's 2005 national champion.
100
Write this sentence as a conditional. A rectangle has four right angles.
If a figure is a rectangle, then it has four right angles.
100
Show that this conditional is false by finding a counterexample: If it is February, then there are only 28 days in the month.
February in the year 2008 is a counterexample. Because 2008 is a leap year, the month of February has 29 days.
100
Draw a Venn Diagram to illustrate this conditional: If you live in Chicago, then you live in Illinios.
See page 81
200
What is a hypothesis?
The part following if, in an if-then statement.
200
What is the hypothesis and conclusion of this conditional statement: If T-38=3, then T=41.
Hypothesis: T-38=3 Conclusion: T=41
200
Write this sentence as a conditional statement. A tiger is an animal.
If something is a tiger, then it is an animal.
200
Show that this is conditional is false by finding a counterexample: If the name of a state contains the word New, then the state borders an ocean.
The conditional is false because New Mexico is a counterexample.
200
Draw a Venn Diagram to illustrate this conditional: If something is a cocker spaniel, then it is a dog.
see page 81
300
What is a conclusion?
The part following then, in an if-then statement.
300
Identify the hypothesis and the conclusion: If two lines are parrallel, then the lines are coplanar.
Hypothesis: Two lines are parrallel. Conclusion: The lines are coplanar.
300
Write as a conditional statement. An integer that ends with 0 is divisible by 5.
If an integer ends with 0, then it is divisible by 5.
300
Find a counterexample to show that this is false: If x^2≥0, then x≥0.
Sample: x=-1
300
Use the Venn Diagram from Venn Diagram for 100. What does it mean to be inside the large circle but outside the small circle?
living in Illinios, but outiside of Chicago.
400
What is the truth value?
Shows whether a conditional statement is true or false. To show that a conditional statement is true, show that every time the hypothesis is true, the conclusion is also true. To show that a conditional is false, you need to find only one counterexample for which the hypothesis is true and the conclusion is false.
400
Write the statement as a conditional: An acute angle measures less than 90.
If an angle is acute, then it measures less than 90.
400
If a figure is a square, then it has 4 congruent sides. Write as a conditional statement. A square has four congruent sides.
If a figure is a square, then it has 4 congruent sides.
400
Write the converse of this conditional statement. Determine the truth value of the conditional and its converse. If two lines do not intersect, then they are parrallel.
If two lines are parrallel, then they do not intersect. The conditional is false and the converse is true.
400
Write the converse of the conditional, and determine the truth value of each: If a^2 = 25, then a =5.
If a=5, then a^2=25; conditional is false;converse is true
500
What is the converse?
The converse of a conditional switches the hypothesis and the conclusion.
500
Write the converse of the following conditional: Conditional: If two lines intersect to form right angles, then they are perpendicular.
Converse If two lines are perpendicular, then they intersect to form right angles.
500
Write the converse of the conditional. If two lines are not parrallel and do not intersect then they are skew.
If two lines intersect to form right angles, then they are perpendicular.
500
Write the converse of this conditional statement. Determine the truth value of the conditional and its converse. If x=2, then l x l =2.
if l x l = 2, then x=2. The conditional is true and the converse is false.
500
See chart on page 82. What is the symbolic form of a conditional and converse statement? How do you read it?
See chart on page 82.