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TUESDAY, AUGUST 21, 2012 TISK Problems 1. Simplify: 2. Evaluate: 3. Simplify: We will have 3 Mental Math Questions today. Homework: p. 81 #20-40 evens

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Page 1: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

TUESDAY, AUGUST 21, 2012

TISK Problems1. Simplify: 2. Evaluate: 3. Simplify:

We will have 3 Mental Math Questions today.

Homework: p. 81 #20-40 evens

Page 2: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

HOMEWORK CHECK15) Sample answer: Points A, B, and C do not lie on a line.16) AB = EF17) Sample answer: X, Y, Z, and W are noncollinear.18) Sample answer: and have a common side and a common vertex.19) Sample Answer: Points R, S, and T are collinear.20) x > 523) False. Counterexample: 24) true; in any rectangle, the opposite sides have to have the same measures.25) false. Counterexample: 26) false; counterexample: If x = -2 then –x = -(-2) = 2.

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Page 3: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

§2.2 CONDITIONAL STATEMENTS

Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part is the hypothesis; the “then” part is the conclusion.

If it is noon in Georgia, then it is 9 A.M. in California.

hypothesis conclusion

Conditional statements can be either true or false. To show that a conditional statement is true, you must prove that for EVERY POSSIBLE case that satisfies the hypothesis, the conclusion is valid. To prove that a conditional statement is false, a single counterexample where the hypothesis is true but the conclusion is invalid is enough proof.

Page 4: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

WRITE EACH OF THE STATEMENTS IN IF-THEN FORM.

All ducks are soft.

The city you visited, Phoenix, is the capital of Arizona.

On Tuesdays, Ms. McEwen assigns Science homework.

Page 5: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

PROVING STATEMENTS WRONG

Write a counterexample to show that the following conditional statement is false.

SOLUTION

Think of a case where x 2 =

16 There are 2: x = – 4 and x = 4.

However, when x = – 4, the conclusion is false (if x = – 4 then it can’t = 4).

This means the given conditional statement is false.

If x 2 = 16, then x = 4.

Page 6: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

NOTATION

We will sometimes use the letters p and q to stand for hypothesis and conclusion.

When this is done, the statement can be simplified to: If

This notation helps us to show other types of statements.

Page 7: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

CONVERSE

A converse is what you get when you flip the hypothesis and conclusion of a statement.

Statement: If Converse: If Example: If it is Saturday, then Miss W

plays video games. Converse: If Miss W plays video games,

then it is Saturday.

Page 8: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

INVERSE

An inverse is obtained by negating the hypothesis and the conclusion of the statement.

Conditional Statement: If Inverse: If Example: If it is Saturday, then Miss W

plays video games. Inverse: If it is not Saturday, then Miss W

does not play video games.

Page 9: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

CONTRAPOSITIVE

• A contrapositive is obtained by negating the hypothesis and the conclusion of the converse.

• Conditional Statement: If • Contrapositive: If • Example: If it is Saturday, then Miss

W plays video games.– Contrapositive: If Miss W does not play

video games, then it is not Saturday.

Page 10: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

TRUTH OF STATEMENTS

When verifying true conditional statements, there are some links! If the original statement is true, its

contrapositive will also be true. If the converse of a statement is true, its

inverse will also be true.

Page 11: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

TRY IT OUT…

For each statement, do the following:a) Rewrite as a conditional statement.b) Determine if it is true.c) Determine which of the other statements (inverse,

converse, contrapositive) are also true.Statement 1: All CPA 9th Grade students wear black socks.

Statement 2: A student who earns 95% has an A.

Statement 3: All lines contain at least two rays.

Statement 4: For every integer value of x less than 4, x is an integer.

Page 12: 15) 17) 18) 1 2 19) 23) 25) Conditional Statement: A conditional statement has two parts, a hypothesis and a conclusion. If-Then Form: the “if” part

HOMEWORK

p. 81 #20-40 evens Yes, there is a lot of writing on this

assignment. If you would prefer to type it, you may do

so.


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