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This document discusses biconditional statements in mathematics. It defines conditional statements, biconditional statements, and related logical concepts like converse, inverse, and contrapositive. Examples are provided to illustrate these concepts. Students are assigned homework problems analyzing conditional and biconditional statements.
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2.2 p2 notes
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This document contains notes from a math class on biconditional statements. It includes:
1) Definitions of conditional statements, converse, inverse, and contrapositive statements.
2) Examples of analyzing whether conditional statements, their converses, inverses, and contrapositives are true or false.
3) An explanation that biconditional statements can be used when a conditional statement and its converse are both true, using "if and only if".
4) Homework assigned from pages 82-83 of problems #16-25 related to conditional and biconditional statements.2.2 p1 notes
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1) The document discusses conditional statements, which are logical statements written in an "if-then" form with a hypothesis and conclusion. Examples of conditional statements and their conversions to inverse, converse, and contrapositive forms are provided.
2) Homework problems are assigned from pages 82 and 83, involving analyzing conditional statements, determining if they are true or false, and identifying definitions as conditional statements.
3) A conditional statement can be written as a biconditional statement using "if and only if" when the conditional statement and its converse are both true. Definitions can also be written as biconditional statements.2.2 definitions and biconditionals
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3) Rewriting conditional statements as biconditional statements using "if and only if".
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2) The converse of a conditional statement switches the hypothesis and conclusion. The inverse negates both parts. The contrapositive obtains the inverse and then switches parts.
3) A biconditional statement uses "if and only if" to join a conditional statement with its converse when both are true. This creates a single statement expressing their relationship.Calc 2.5b
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It provides examples of writing conditional statements as biconditional statements using "if and only if". It also gives examples of writing the converse, negation, inverse, and contrapositive of conditional statements. The document instructs the reader to write 5 conditional statements and find the converse, negation, inverse, and contrapositive of each.Star teurope@europrix conference
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cow
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This document discusses conditional statements and their analysis. It defines conditional statements as logical statements written in if-then form with a hypothesis and conclusion. It explains how to determine if a conditional statement is true or false by considering the converse, inverse, and contrapositive. Conditional statements can be used to write definitions. Biconditional statements can be used when the conditional statement and its converse are both true. The document provides homework problems for students to practice these concepts.2.2 p2 notes
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This document contains notes from a math class on biconditional statements. It includes:
1) Definitions of conditional statements, converse, inverse, and contrapositive statements.
2) Examples of analyzing whether conditional statements, their converses, inverses, and contrapositives are true or false.
3) An explanation that biconditional statements can be used when a conditional statement and its converse are both true, using "if and only if".
4) Homework assigned from pages 82-83 of the textbook problems #3-5, 7-15, 31-32 and #16-18.2.2 p1 notes
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Ìý
1) The document discusses conditional statements, which are logical statements written in an "if-then" form with a hypothesis and conclusion. Examples of conditional statements and their conversions to inverse, converse, and contrapositive forms are provided.
2) Homework problems are assigned from pages 82 and 83 that involve analyzing and converting conditional statements.
3) A conditional statement can be true or false, and its truth value depends on whether the conclusion is true every time the hypothesis is true. Definitions can also be written as conditional or biconditional statements.Geom 2point1
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This document discusses conditional statements and their components. It defines a conditional statement as having a hypothesis and conclusion connected by "if...then". It provides examples of writing the converse, inverse, and contrapositive of conditional statements. The key points are:
- A conditional statement has two parts: a hypothesis and conclusion connected by "if...then"
- The converse switches the hypothesis and conclusion
- The inverse negates both the hypothesis and conclusion
- A statement is equivalent to its contrapositive
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1) Definitions of conditional statements, converse, inverse, and contrapositive statements.
2) Examples of analyzing whether conditional statements, their converses, inverses, and contrapositives are true or false.
3) An explanation that biconditional statements can be used when a conditional statement and its converse are both true, using "if and only if".
4) Homework assigned from pages 82-83 of the textbook problems #3-5, 7-15, 31-32 and #16-18.2.2 p1 notes
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2) Homework problems are assigned from pages 82 and 83 that involve analyzing and converting conditional statements.
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- The converse switches the hypothesis and conclusion
- The inverse negates both the hypothesis and conclusion
- A statement is equivalent to its contrapositiveLECTUdfvdfvdfvRvdf conditvdfvional.ppt
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2.2 p2 notes
- 1. 2.2 Biconditional Statements September 06, 2011 Bellwork 1. What is the definition of conjecture? A guess based on observation 2. Write the next number in the sequence 1, 5, 9, 13,... 17 3. A _______ disproves a conjecture. counterexample 4. (Â4)( 7)+2 Â1=? Â27 5. Are you lost yet in chapter 2? HW pg. 83 #16Â25 1
- 2. 2.2 Biconditional Statements September 06, 2011 2.2 Analyze Conditional Statements Conditional Statement: logical statement that has 2 parts-hypothesis & conclusion written in if-then form Ex. If it is raining, then there are clouds in the sky. Rewrite the conditional statement in if-then form. All birds have feathers. If an animal is a bird, then it has feathers. 2 angles are supplementary if they are a linear pair If 2 angles are a linear pair, then they are supplementary. HW: pg 82 #3-5 HW pg. 83 #16Â25 2
- 3. 2.2 Biconditional Statements September 06, 2011 · Conditional statements can be T or F. · Prove that the conclusion is true every time the hypothesis is true. · To show false: give 1 counterexample. Negation: Opposite of original statement Original: Ball is red. Negation: Ball is not red. Conditional Statement: If m A = 99, then A is obtuse. T Converse: exchange the hypothesis and conclusion If m A is obtuse, then m A = 99. F Inverse: negate both the hypothesis and conclusion If m A ≠99, then A is not obtuse. F Contrapositive: write the converse, then negate both hypothesis and conclusion If A is not obtuse, then m A ≠99. T HW pg. 83 #16Â25 3
- 4. 2.2 Biconditional Statements September 06, 2011 HW: pg. 82 #3-5,7-15,31 & 32 HW pg. 83 #16Â25 4
- 5. 2.2 Biconditional Statements September 06, 2011 You can write a definition as a conditional statement in if-then form or as its converse. Both are True. Definition: If 2 lines intersect to form a right angle, then they are perpendicular lines. Converse: If 2 lines are perpendicular, then they intersect to form a right angle. You can write "line l is perpendicular to line m" as l m. l m HW pg. 83 #16-18 HW pg. 83 #16Â25 5
- 6. 2.2 Biconditional Statements September 06, 2011 Biconditional Statement: · When conditional statement and converse are T, then you can write them as a biconditional statement. · if and only if (IFF) · any valid definition can be written as biconditional HW pg. 83 #16Â25 6
- 7. 2.2 Biconditional Statements September 06, 2011 HW pg. 83 #16Â25 7
- 8. 2.2 Biconditional Statements September 06, 2011 HW pg.83 #16-25 HW pg. 83 #16Â25 8