Chapter 2 Review

Conditional StatementsLaws of Logic

VocabularyConditional statement

If-then form

Hypothesis

Conclusion

Negation

VocabularyConverse

Inverse

Contrapositive

Equivalent Statements

Biconditional Statement

Rewrite the conditional statement in if-then form.

All vertebrates have a backbone.

All triangles have three sides.

When x = 2, x² = 4.

Rewrite the conditional statement in if-then form.

I use my umbrella when it rains.

The back-up lights are on when a car is in reverse.

You will get coal in your stocking if you’ve been naughty.

Write four related conditional statements.Write the if-then form, the converse, the inverse, and the contrapositive of the conditional statement “Olympians are athletes.” Decide whether each statement is true or false.

Write four related conditional statements.Write the if-then form, the converse, the inverse, and the contrapositive of the conditional statement “Squares are rectangles.” Decide whether each statement is true or false.

Write four related conditional statements.Write the if-then form, the converse, the inverse, and the contrapositive of the conditional statement “Running a marathon is exhausting.” Decide whether each statement is true or false.

Write a BiconditionalTo write a definition as a biconditional, first write the statement in if-then form.

Next, write the converse of the if-then statement.

Finally, combine the two statements with “if and only if”.

Write the definition of parallel lines as a biconditional.Definition: If two lines lie in the same plane and do not intersect, then they are parallel.

Decide whether the statement is true or false. If false, provide a counterexample.

Decide whether the statement is true or false. If false, provide a counterexample.

Read the statement, then the phrase. Tell if the phrase is the hypothesis or conclusion.

1. If you build it then they will come.you build it

2. If two lines in a plane are parallel then they will not intersect.they will not intersect

3. If you fill your sink with water then you can wash the dishes.you can wash the dishes

Read the statement, then the phrase. Tell if the phrase is the hypothesis or conclusion.

1. If a triangle has a right angle then it is a right triangle.a triangle has a right angle

2. If an angle measures 24° then it is acute.it is acute

3. If you are a fish then you live in the water.you are a fish

Symbolic NotationConditional statements can be written using symbolic notation, where p represents _____________________ ,

q represents _________________________ ,

and → is read as __________________________ .

Symbolic NotationIf p → q represents a conditional statement, use symbolic notation to represent the converse, inverse, contrapositive and biconditional.

Symbolic Notation

Laws of LogicWrite the following laws of logic using symbolic notation.

Modus Ponens

Modus Tollens

Law of Syllogism

Law of Contrapositive

Laws of LogicWhich law of logic is represented?

p → q, q → r, p → r

p → q, ~q, ~p

p → q, ~q → ~p

p → q, p, q

Laws of LogicTranslate each argument into symbolic form and identify the rule that makes it valid.

If Jed gets a C on the exam, then he will get an A for the semester. Jed got a C on the exam. Jed will make an A for the semester.

Laws of LogicTranslate each argument into symbolic form and identify the rule that makes it valid.

If the car is running, then the key is in the ignition. The key is not in the ignition. The car is not running.

Laws of LogicTranslate each argument into symbolic form and identify the rule that makes it valid.

If Marie cooks, then there is smoke. There is not smoke, so Marie is not cooking.

Laws of LogicTranslate each argument into symbolic form and identify the rule that makes it valid.

If Mike visits Alabama, then he will spend the day in Montgomery. If Mike spends the day in Montgomery, then he will visit the Civil Rights Memorial. If Mike visits Alabama, then he will visit the Civil Rights Memorial.