section 2-2 biconditional statements. biconditional statement a statement that contains the phrase...

Section 2-2 Bicondition al Statements

Upload: kristin-russell

Post on 17-Jan-2016

220 views

Category:

Documents

2 download

Report

Download

Embed Size (px):

TRANSCRIPT

Section 2-2Biconditional Statements

Biconditional statement

• a statement that contains the phrase “if and only if”.

• Equivalent to a conditional statement and its converse.

We can use iff to stand for “If

and only if”

In order for a biconditional

statement to be TRUE, both the conditional

statement and its converse must be

true.

Page 5: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

Example #1:

• Two lines intersect if and only if their intersection is exactly one point.

Write this biconditional statement as a conditional statement.

Page 6: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

• If two lines intersect, then

their intersection is exactly

one point. True

Conditional Statement:

• If their intersection is exactly one point, then two lines intersect.

Now write the converse.

True

Page 8: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

Example #2

• Three lines are coplanar if and only if they lie in the same plane.

Write this biconditional statement as a conditional statement.

•If three lines are coplanar, then they lie in the same plane. True

Conditional Statement:

•If three lines lie in the same plane, then they are coplanar.

Now write the converse.

True

Page 11: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

• If an angle is acute then it has a measure between 0° and 90°.

Write the conditional as a biconditional statement.

Page 12: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

Write the converse

• If an angle has a measure between 0° and 90°, then it is acute. True

Page 13: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

• If it is true, then a biconditional can be written

• If it is false, then a biconditional CAN NOT be written.

Identify whether the converse is true or false

Page 14: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

Bicondtional:• An angle is acute if and only if it has a measure between 0° and 90°.

Page 15: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

• If an animal is a leopard, then it has spots.

Write the conditional as a biconditional statement.

Write the converse.• If an animal has spots, then

is a leopard. False

Page 16: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

Therefore a biconditional for this statement does not exist!

Page 17: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

More Examples:Try It!

Write each conditional as a biconditional statement, if possible. Be sure to give a counterexample if the converse is false!

Page 18: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

1.If is perpendicular to , then their intersection forms a right angle.SR QR

Converse:

If, and intersect at a right angle, then they are perpendicular to each other.

SR QR

True

Page 19: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

• is perpendicular to

iff their intersection forms a right angle.

Biconditional: SR QR

Page 20: Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement

2. If x2 < 49, then x < 7

If x < 7, then x2 < 49.

8x• Counterexample: let then 498 2

Therefore, a biconditional

can not be written!

Converse:

2-4 Biconditional statement. Objectives Write and analyze biconditional statements

The if Statement

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

If statement

Holt Geometry 2-4 Biconditional Statements and Definitions Warm Up Write a conditional statement from each of the following. 1. The intersection of two

if statement formats

Holt Geometry 2-4 Biconditional Statements and Definitions Warm Up: For the given statement, determine the converse, inverse, and contrapositive. Assuming

5 if Statement

LESSON 4 Decision Control Structure. Decision Control Structures 1. if statement 2. if-else statement 3. If-else-if statement 4. nested if statement 5

Java If-else Statement · Java If-else Statement The Java if statement is used to test the condition. It checks Boolean condition: true or false.There are various types of if statement

Section 3.3 Truth Tables for the Conditional and Biconditional

Biconditional Statements and Definitions · 2-4 Biconditional Statements and Definitions Check It Out! Example 1b Cho is a member if and only if he has paid the $5 dues. Write the

2.3 Deductive Reasoning p. 87 Reminders Statement Conditional statement Converse Inverse Contrapositive Biconditional Symbols p → q q → p ~p → ~q ~q

Tools of Geometry Chapter 1 - ahodginscc · Tools of Geometry Chapter 1 Undefined Terms ... Midpoint Formula ... A biconditional statement is the conjunction of a conditional and

1 CS 1430: Programming in C++. 2 IF Statement if (cond) statement //Next statement if (cond) { statement1 statement2 … } //Next statement

Chapter 3:Decision Structures. 3.1 The if Statement 3.2 The if-else Statement 3.3 The if-else-if Statement 3.4 Nested if Statements 3.5 Logical

Write and analyze biconditional statements

Deductive Reasoning and Biconditional Statements · 2014. 1. 24. · For example: If you get caught chewing gum, then you get a Saturday school. If you study your power cards, notes,

Edl · Rewrite the definition of congruent segments (shown below) as a single biconditional statement: "If two line segments have the same length, then they are congruent segments

3 2. if statement

Conditional and biconditional statements

Holt Geometry 2-4 Biconditional Statements and Definitions Write and analyze biconditional statements. Objective

Implication and Biconditional in some Three-valued Logics

Geometry - Mr Hickman's Class 2020-2021...September 7, 2016 GEOMETRY 2.1 CONDITIONAL STATEMENTS. Write the following biconditional statement as a conditional statement and its converse

Approved by the Vice-Chancellor dated 27.06. Sc. Geophysics 2019-20ab.pdfIF statement, IF…. ELSE statement, nested IF, GOTO statement, break statement, CONTINUE statement, ... Wiener

buttefallsmath.weebly.combuttefallsmath.weebly.com/uploads/2/3/3/6/23368334/geo2work.pdf · Geometry Chapter 2 Study Guide ... Write the biconditional statement of the conditional

Logic: Conditional & Biconditional · Josh Engwer (TTU) Logic: Conditional & Biconditional 21 July 2015 28 / 33 Converses, Inverses, Contrapositives of Conditionals WEX 3-3-3: Given

Geometry A curr map.pdf · Week 5 C.I.a: Use definitions ... conditional statement ... conclusion converse inverse 9. contrapositive Biconditional statement 10. Deductive reasoning

Chapter 9 IF Statement

Bell Work “If x=4, then “ 1)Write the hypothesis 2)Write the Conclusion 3) Write the converse 4)What is the Biconditional?

Conditional Statement A statement that can be written in If-Then form If-Then Statement Statement written in the form If p, then q. Hypothesis

Chapter 3 Decision Structures 1. Contents 1.The if Statement 2.The if-else Statement 3.The if-else-if Statement 4.Nested if Statement 5.Logical Operators

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

If Statement Tracing

Chapter 4: Making Decisions. Outline Relational Operations If statement – If – If/else statement – If/else if Logical operators Switch