2-3 conditional statements you used logic and venn diagrams to determine truth values of negations,...

2-3 Conditional Statements

You used logic and Venn diagrams to determine truth values of negations, conjunctions, and disjunctions.

• Analyze statements in if-then form.

• Write the converse, inverse, and contrapositive of if-then statements.

Conditional Statements

• Her condition improved each day she exercised.

• Mom said I could go to the mall on one condition.

• If I taped my ankle each morning, then the condition of it would improve.

In mathematics, statements in if-then form are called conditional statements.

Parts of a Conditional Statement

• I wrote my hypothesis for my Science Fair project.

• The experiment proved my hypothesis wrong.

• I had a good conclusion at the end of my English paper.

• I came to the conclusion that I lost my notebook.

Parts of a Conditional Statement

Hypothesis—the if part of a conditional statement.

Conclusion—the then part of a conditional statement.

Write a Conditional Statement

Hypothesis: You talk on the telephone more than one hour per night.

Conclusion: Your grade will drop one letter.

If you talk on the telephone more than one hour per night, then your grade will drop one letter.

Identify the Hypothesis and Conclusion

A. Identify the hypothesis and conclusion of the following statement.

Answer: Hypothesis: A polygon has 6 sides.Conclusion: It is a hexagon.

If a polygon has 6 sides, then it is a hexagon.

If a polygon has 6 sides, then it is a hexagon.

hypothesis conclusion

Identify the Hypothesis and Conclusion

B. Identify the hypothesis and conclusion of the following statement.

Tamika will advance to the next level of play if she completes the maze in her computer game.

Answer: Hypothesis: Tamika completes the maze in her computer game.Conclusion: She will advance to the next level of play.

A. Hypothesis: You will cry.Conclusion: You are a baby.

B. Hypothesis: You are a baby.Conclusion: You will cry.

C. Hypothesis: Babies cry.Conclusion: You are a baby.

D. none of the above

A. Which of the choices correctly identifies the hypothesis and conclusion of the given conditional?

If you are a baby, then you will cry.

Conditional statements are not always in if-then form, but any statement can be rewritten in that form.

It is easier to identify the hypothesis and conclusion when it is written in if-then form.

A. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form.Measured distance is positive.

Answer: Hypothesis: A distance is measured.Conclusion: It is positive.If a distance is measured, then it is positive.

Write a Conditional in If-Then Form

Write a Conditional in If-Then Form

B. Identify the hypothesis and conclusion of the following statement. Then write the statement in the if-then form.

A five-sided polygon is a pentagon.

Answer: Hypothesis: A polygon has five sides.Conclusion: It is a pentagon.If a polygon has five sides, then it is a pentagon.

Do Television commercials use Conditional Statements?

True or False?For a conditional statement to be true, the

conclusion must be true whenever the hypothesis is true. A conditional is false only if there is a case in which the hypothesis is true and the conclusion is false.

If two numbers are both odd, then their sum is odd.

The condition is false because the conclusion is false even though the hypothesis is true.

Truth Values of ConditionalsA. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.

If you subtract a whole number from another whole number, the result is also a whole number.

Answer: Since you can find a counterexample, the conditional statement is false.

Counterexample: 2 – 7 = –5

2 and 7 are whole numbers, but –5 is an integer, not a whole number.

The conclusion is false.

Truth Values of ConditionalsB. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.

If last month was February, then this month is March.

Answer: So, the conditional statement is true.

When the hypothesis is true, the conclusion is also true, since March is the month that follows February.

A. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.The product of whole numbers is greater than or equal to 0.A. True; when the

hypothesis is true, the conclusion is also true.

B. False; –3 ● 4 = –12

B. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.If yesterday was Tuesday, then today is Monday.

A. True; when the hypothesis is true, the conclusion is false.

B. False; today is Wednesday.

C. Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample.If a triangle has four right angles, then it is a rectangle.

A. True; the hypothesis is false, and a conditional with a false hypothesis is always true.

B. False; a right triangle has one right angle.

2-3 Assignment

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