Chapter 2: If Then Statements and Converses

Lila del Risco
Note by Lila del Risco, updated more than 1 year ago
Lila del Risco
Created by Lila del Risco over 2 years ago


Notes on "If Then" statements.

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Conditional Statements Conditionals are very important in any discipline that uses logic If, Then< conclusion> *Usually the hypothesis follows the If and the conclusion follows the Then Ways to Write a Conditional If p then q q if p p => q Implied Then Sometimes you may not see the "Then" in a conditional. This is called the implied Then. Eg. If I drink my milk,  I'll grow to be tall Sometimes there is no If and there is no Then Eg. If I don't study for my test, Then I will fail Converse- the converse of a conditional statement is a conditional whose hypothesis and conclusion have been interchanged Original                                                                                                                     Converse   P: I die today   Q: I'll be the happiest person alive 1. If p Then q- If I die today then I'll be the happiest person alive             1. If I'm the happiest person alive then I'll die today 2. q if p- I'll be the happiest person if I die today                                            2. I'll die today if I'm the happiest person alive 3. p => q- Dying today implies I'll be the happiest person alive                  3. Being the happiest person alive implies I'll die today                                                                                                                       Page 1

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Venn Diagram (Refer to Google Docs)   Biconditional Statements-  A biconditional statements is a conditional whose converse has the same truth value as the original conditional Biconditional statements always contain the phrase "if and only if" (iff). Eg. Original: If three points are collinear then the points are on the same line       Converse: If three points are on the same line then they are collinears       Bi-conditional: Three points are collinear if and only if they are on the same line       Bi-conditional Symbol- p <=> q *The if is never part of the hypothesis 1. All months have at least 30 days- False: February 28 or 29 days 2. If a line is contained in a plane, then that plane is unique- False: A line can be contained in various planes 3. All rectangles are squares- False: Squares must have four equilateral sides  4. If the m False: It could be a straight angle    

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Classroom Exercises 1. H: 2x-1=5   2. H: She's smart    3. H: 8y=40     4. H: S is the midpoint of line RT         C: x=3              C: I'm a genius       C: y=5              C:  RS= 1/2RT    

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