Lesson 2.3

CONDITIONAL STATEMENTS

CONDITIONAL STATEMENTS

• KEYWORDS

• Conditional statement – a statement that can be written in “if…then…” form.

• If-then statement – the form “if p, then q”, or “p implies q”

• Hypothesis – the phrase immediately following the word “if”

• Conclusion - the phrase immediately following the word “then”

CONDITIONAL STATEMENTS

• For example:

• If you had a statement…

• If the forecast is rain, then I will take an umbrella.

• The hypothesis:

• The conclusion:

CONDITIONAL STATEMENTS

• For example:

• If you had a statement…

• A number is divisible by 10 if its last digit is a 0.

• Hypothesis:

• Conclusion:

CONDITIONAL STATEMENTS

• But, what if the statement didn’t have “if…then…” in it?

• For example:

• The statement might read: “Points will be deducted from any paper turned in after Wednesday’s deadline.

• In this case, the hypothesis is: paper turned in after Wednesday’s deadline. The conclusion is: points will be deducted.

CONDITIONAL STATEMENTS

• Practice: (you write the conditional)

• Hypothesis: An animal is a mammal

• Conclusion: It is warm-blooded

• Hypothesis: A prism has bases that are regular polygons.

• Conclusion: It is a regular prism

CONDITIONAL STATEMENTS

• The hypothesis and the conclusion of a conditional statement can have a truth value of true or false, as can the conditional statement itself. Consider the following conditional.

CONDITIONAL STATEMENTS

• If Tom finishes his homework, then he will clean his room.

CONDITIONAL STATEMENTS

• In the last two: The conditional only indicates what will happen if Tom DOES finish his homework. It never states what will happen if he DOESN’T do his homework. He could clean his room or not clean his room if he does not finish his work.

• When the hypothesis of a conditional is not met, the truth of a conditional cannot be determined. When the truth of a conditional statement cannot be determined, it is considered TRUE by default.

CONDITIONAL STATEMENTSCONDITIONAL STATEMENTS

p q if p then qT T TT F FF T TF F T

Notice that a conditional is false ONLY when its hypothesis is true and its conclusion is false.

Notice too that when a hypothesis if false, the conditional will ALWAYS be considered true, regardless of whether the conclusion is true of false

CONDITIONAL STATEMENTS

• Determine the truth value for each statement:

• If you divide an integer by another integer, the result is also an integer.

CONDITIONAL STATEMENTS p q if p then qT T TT F FF T TF F T

CONDITIONAL STATEMENTS

• Determine the truth value for each statement:

• If a triangle has four sides, then it is concave.

CONDITIONAL STATEMENTS p q if p then qT T TT F FF T TF F T

CONDITIONAL STATEMENTS

CONDITIONAL STATEMENTS