MIDTERM REVIEW PROJECT:

CONDITIONAL STATEMENTS

NAME REMOVED

WHAT IS A CONDITIONAL STATEMENT?A conditional statement is an if-then statement.

•If is the hypothesis

•Then is the conclusion

•If p then q

p q

CONVERSE

The converse of a conditional statement is created by switching the hypothesis and the conclusion in a conditional statement.

• q p

•If q, then p

INVERSE

The inverse of a conditional statement is created by negating the hypothesis and negating the conclusion.

NOT is usually inserted in front of both the hypothesis and conclusion

•~p ~q

•~ : represents not

•If not p, then not q

CONTRAPOSITIVE

The contrapositive of a conditional statement is created by combining the inverse and the converse. (Switch the hypothesis and conclusion and add not in front of both)

•~q ~p

•If not q, then not p

LAWS RELATED TO CONDITIONAL STATEMENTS Biconditional Statements- A conditional statement whose converse is also true.

The Law of Detachment- If the conditional statement is true, and the hypothesis is true, then the conclusion is true.

The Law of Syllogism- If p then q, if q then r. Therefore p, then r.

Remember p is the hypothesis, q is the conclusion, and r is a new variable.

TIPSLeft hand= hypothesis Right hand= conclusion

Conditional:

Left hand and right hand

Converse:

Left hand and right hand cross over

Inverse:

Left hand and right hand flipped over

(The Beyoncé)

Contrapositive:

Left hand and right hand switch as well as flip over

(The Napolean Dynamite)

Conditional Statement

Inverse

Converse

Contrapositive

EXAMPLE 1 Directions:

Read the statement provided

Locate the hypothesis and conclusion

Solve

Problem:

If James watches TV instead of studying for his test, then he will fail.

What is the inverse of this statement?

Explanation:

An inverse is created by adding not in front of the hypothesis and the conclusion

So the answer is…

If James does not watch TV instead of studying for his test, then he will not fail.

EXAMPLE 2 Directions:

Read the statement provided

Locate the hypothesis and conclusion

Solve

Problem:

If you are a fan of Beyoncé, then you are in the Bey Hive.

What is the converse of this statement?

Explanation:

The converse of a conditional statement is created by switching the hypothesis and conclusion.

So the answer is…

If you are in the Bey Hive, then you are a fan of Beyoncé.

PRACTICE PROBLEM 1

If I eat 4 bags of chips before a basketball game, then I will throw up.

What is the inverse of this statement?

PRACTICE PROBLEM 2

If Adam quits his job, then he will be broke.

What is the contrapositive of this statement?

PRACTICE PROBLEM 3

If you are a Beyoncé hater, then you are considered a wasp.

What is the converse of this statement?

PRACTICE PROBLEM 4

If Kass gets sick, then she can’t come to school.

What is the inverse of this statement?

PRACTICE PROBLEM 5

If I get ice-cream and pizza, then I will be satisfied.

What is the converse of this statement?

SOLUTIONS

Problem 1: If I do not eat 4 bags of chips before a basketball game, then I will not throw up.

Problem 2: If Adam is not broke, then Adam did not quit his job.

Problem 3: If you are considered a wasp, then you are a Beyoncé hater.

Problem 4: If Kass does not gets sick, then she can come to school.

Problem 5: If I’m satisfied, then I got ice-cream and pizza.

CITATIONS

http://www.celebuzz.com/2014-08-22/beyonce-birthday-flashback/

https://girlbehindthebooks.wordpress.com/2014/02/17/a-different-view-on-lamour/

http://www.ucl.ac.uk/news/news-articles/1105/11052001

http://specialreports.com/emnapoleon-dynamiteems-10th-b-day-enjoy-these-sweet-gifs/

http://hotmath.com/hotmath_help/topics/converse-inverse-contrapositive.html