Upload File

lesson 2-1 conditional statements. conditional statement defn. a conditional statement is a...

  • Home
  • Documents
  • Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That
36
Lesson 2-1 Conditional Statements

Upload: spencer-hamilton

Post on 02-Jan-2016

244 views

Category:

Documents


2 download

Report

TRANSCRIPT

Page 1: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Lesson 2-1

ConditionalStatements

Page 2: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Conditional Statement

Defn. A conditional statement is a statement that can be written as an if-then statement. That is, as

“If _____________, then ______________.”

Page 3: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example:

If your feet smell and your nose runs,

then you're built upside down.

Page 4: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Conditional Statements have two parts:

The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.)

It is the given information, or the condition.

If a number is prime, then a number has exactly two divisors.

Hypothesis: a number is primeLeave off “if” and comma.

Page 5: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Conditional Statements have two parts:

The conclusion is the part of a conditional statement that follows “then” (when written in if-then form.)

It is the result of the given information.

If a number is prime, then a number has exactly two divisors.

Conclusion: a number has exactly two divisors

Leave off “then” and period

Page 6: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Conditional statements can be put into an “if-then” form to clarify which part is the hypothesis and which is the conclusion.

Method: Turn the subject into a hypothesis.

Rewriting Conditional Statements

Page 7: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example 1:

Vertical angles are congruent.

If two angles are vertical, then they are congruent.

can be written as...

Page 8: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example 2:

Seals swim.

If an animal is a seal, then it swims.

can be written as...

Page 9: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example 3:

Babies are illogical.

If a person is a baby, then the person is illogical.

can be written as...

Page 10: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

IF …THEN vs. IMPLIES

Two angles are vertical implies they are congruent.

Another way of writing an if-then statement is using the word implies.

Page 11: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Conditional Statements

can be true or false:• A conditional statement is false

only when the hypothesis is true, but the conclusion is false.

• A counterexample is an example used to show that a statement is not always true and therefore false.

Page 12: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Counterexample

Therefore () the statement is false.

Statement: If you live in Virginia, then you live in Richmond, VA.

Is there a counterexample?

YES... Anyone who lives in Virginia, but not Richmond, VA.

Page 13: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Symbols can be used to modify or connect statements.

Symbolic Logic

Page 14: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Symbols for Hypothesis and Conclusion

if p, then q or

p implies q

Lower case letters, such as p and q, are frequently used to represent the hypothesis and conclusion.

Page 15: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Symbols for Hypothesis and Conclusion

if p, then q or p implies q

Examplep: a number is prime

q: a number has exactly two divisors

If a number is prime, then it has exactly two divisors.

Page 16: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

is used to represent the words

“if … then”or

“implies”

Page 17: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

p q

if p, then q

or

p implies q

means

Page 18: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example

p: a number is prime q: a number has exactly two divisorspq: If a number is prime, then

it has exactly two divisors.

Page 19: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

is used to represent the word

“not”

~

•~ p is the negation of p.•The negation of a statement is the denial of the statement. Add or remove the word “not.”•To negate, write ~ p.

Page 20: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example

p: the angle is obtuse

~p: the angle is not obtuse

Be careful because ~p means that the angle could be acute, right, or straight.

Page 21: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example

p: James doesn’t like fish.

~p: James likes fish.

Notice: ~p took the “not” out… it would have been a double negative (not not)

Page 22: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

is used to represent the word

“and”

Page 23: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example

p: a number is even q: a number is divisible by 3

pq: A number is even and it is divisible by 3.

6,12,18,24,30,36,42...

Page 24: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

is used to represent the word

“or”

Page 25: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example

p: a number is even q: a number is divisible by 3

pq: A number is even or it is divisible by 3.

2,3,4,6,8,9,10,12,14,15,...

Page 26: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

is used to represent the word

“therefore”

Page 27: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Example

Therefore, the statement is false.

the statement is false

Page 28: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Different Forms of Conditional Statements

Page 29: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Forms of Conditional Statements

Converse: Statement formed from a conditional statement by switching the hypothesis and conclusion (q p)

pq If two angles are vertical, then they are congruent.

qp If two angles are congruent, then they are vertical.

Continued…..Are these statements true or false?

Page 30: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Forms of Conditional Statements

Inverse: Statement formed from a conditional statement by negating both the hypothesis and conclusion.

(~p~q)

pq : If two angles are vertical, then they are congruent.

~p~q: If two angles are not vertical, then they are not congruent.

Are these statements true or false?

Page 31: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Forms of Conditional Statements

Contrapositive: Statement formed from a conditional statement by switching and negating both the hypothesis and conclusion.

(~q~p)

pq : If two angles are vertical, then they are congruent.

~q~p: If they are not congruent, then two angles are not vertical

Are these statements true or false?

Page 32: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Contrapositives are logically equivalent to the original conditional statement.

• If pq is true, then qp is true.

• If pq is false, then qp is false.

Page 33: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Biconditional • When a conditional statement and its

converse are both true, the two statements may be combined.

• A statement combining a conditional statement and its converse is a biconditional.

• Use the phrase if and only if which is abbreviated iff

• Use the symbol

Page 34: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Definitions are always biconditional

Statement: pq If an angle is right then it measures 90.Converse: qp If an angle measures 90, then it is right.Biconditional: pq An angle is right iff it measures 90.

Page 35: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Biconditional • A biconditional is in the form:Hypothesis if and only if Conclusion.

orHypothesis iff Conclusion

or

Hypothesis Conclusion

Page 36: Lesson 2-1 Conditional Statements. Conditional Statement Defn. A conditional statement is a statement that can be written as an if- then statement. That

Biconditionals in symbols

Since p q means pq AND qp,

p q Is equivalent to(pq) (qp)


Conditional Statement

Part 2 Module 2 The Conditional Statement. The Conditional Statement A conditional statement is a statement of the form "If p, then q," denoted pqpq

Nested conditional statements. A conditional statement (i.e., an if-statement or an if-else- statement) is also a statement We can use an if-statement

Conditional statement ss1

2.1 Conditional Statements. Conditional Statement Conditional statement has two parts, hypothesis and a conclusion. If _____________, then____________

2.1 Conditional Statements Goals Recognize a conditional statement Write postulates about points, lines and planes

Chapter 2.3 Conditional Statements. Conditional Statement

Conditional statement in java

MGCUB, INDIA Conditional Statement-I · 2020. 4. 29. · M3 Conditional Statement-I Mr. J. Mishra MGCUB, INDIA Objectives Introduction if Statement Multiple if Statement if …else

Intruduction conditional statement

Nopol: Automatic Repair of Conditional Statement Bugs in ... · Nopol: Automatic Repair of Conditional ... Automatic Repair of Conditional Statement Bugs in Java ... This extension

4. Conditional Probability - University of Washington€¦ · conditional probability General defn: where P(F) > 0 Holds even when outcomes are not equally likely. “P( - | F )”

Ocw Newsletter Januari2010 Defn

JavaScript V Conditional Execution. Outline Conditional statement If-then If-then-else Nested If Boolean expressions

 · Every conditional statement has three related conditional statements. Geometry (H) ... 11. Write three separate conditional statements that the Venn diagram illustrates

2.2 Write Definitions as Conditional Statements. Conditional Statement A logical statement with a hypothesis and a conclusion. If-then form: “If” part

Alejandro Gonzalez M2 Algebra Geo Journal 2. Conditional if then statements A conditional statement or if then statements is a statement written in the

Geometry: 2.1-2.3 Notes · 2 Conditional Statement A conditional statement is a logical statement that has two parts, a hypothesis p and a conclusion q. When a conditional statement

2.3 Conditional Statements 0 Conditional statement- a statement that can be written in if-then form

Chapter 2. Sanguk Noh - cis.catholic.ac.krcis.catholic.ac.kr/sunoh/Courses/DiscreteM/DMChapter2.pdf · Conditional statements Conditional statements Conditional statement or implication

FAA POLICY STATEMENT: Limited, Conditional Extension ......1 FAA POLICY STATEMENT: Limited, Conditional Extension of COVID-19 Related Relief at Chicago O’Hare International Airport,

Conditional Statements - Mrs. Barnhart's Classesswhsbarnhart.weebly.com/uploads/8/6/9/5/86959108/geo_02_01.pdf · A conditional statement is a logical statement that has two parts,

Section 2.2 Conditional Statements 1 Goals Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional

1.Defn , Role & Importance

Conditional Statement Chapter 8. Conditional Statements Are statements that check an expression then may or may not execute a statement or group of statement

Part 2 Module 2 The Conditional Statement

Tra.escri.ope.met defn

Completed Conditional and Biconditional Statements Notes€¦ · Conditional and Biconditional Statements Conditional Statement: a statement written in if-then form. The “if”

Colitis Ulcerativa Expo Defn

Conditional Statement in C Language

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the

Nested conditional statements. Previously discussed Conditional statements discussed so far: Syntax of the if-statement: if-statement if-else-statement

Conditional Statement & Loops

2.2 Conditional Statements. Goals Identify statements which are conditional Identify the antecedent and consequent of a conditional statement Negate conditional

2.2 – Analyze Conditional Statements. Conditional Statement Hypothesis Conclusion Logical statement written in if-then form. If p, then q. pqpq Statement