University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

415

Pages:

3
Author:

Omari Mccormick

Conditional Statements List of terms you should understand and recognize in word and symbol notation (as covered in class). conditional statement a logical statement that has two parts, a hypothesis paind a conclusion q. if-then form how we write conditional statements Words "If then q" Symbols p4 hypothesis the "if" part of the conditional statement conclusion the "then" part of the conditional statement negation the opposite of the original statement. Words "not g" converse exchange the hypothesis and the conclusion Symbols Words "If q, then p Inverse negate both the hypothesis and the conclusion. Words "If not then not q" Symbols Symbols contrapositive exchange AND negate the hypothesis and the conclusion Words "If not q, then not Symbols equivalent statements. two statements (conditional and its contrapositive) are both true or both false hiconditional statement one statement that combines a (true) conditional and its converse statements together. Words "pif and only if q" Symbols truth value a "true" OR "false" evaluation of a statement truth table a table that shows the truth values for " and the "g" Conditional statements are not always true. 2.1 Extra Practice Instructions: In Exercises 1 and 2, rewrite the conditional statement in if-then form. Exercise 1: Original Statement: 13x - 5 = -18 because x = -1 Rewritten Statement: If x = -1 then 13x - 5 = -18 Exercise 2: Original Statement: The sum of the measures of interior angles of a triangle is 180° Rewritten Statement: If you have a triangle then the sum of the measures of interior angles is 180° Additional note: "* think about what you start with" Exercise 3: Given: Let p be "Quadrilateral ABCD is a rectangle" Let q be "the sum of the angle measures is 360°" Task: Write the (and decide if each is true or false) Conditional Statement: Symbolic form: p → q Statement: If quadrilateral ABCD is a rectangle then the sum of the angle measures is 360° Truth Value: True Converse Statement: Symbolic form: q → p Statement: If the sum of the angle measures is 360° then quadrilateral ABCD is a rectangle. Truth Value: False Inverse Statement: Symbolic form: ~p → ~q Statement: If quadrilateral ABCD is not a rectangle then the sum of the angle measures is not 360° Truth Value: False Contrapositive Statement: Symbolic form: ~q → ~p Statement: If the sum of the angle measures is not 360° then quadrilateral ABCD is not a rectangle Truth Value: True 2.1 Extra Practice Instructions: In Exercises 4-6, decide whether the statement about the diagram is true. Explain your answer using the definitions you have learned. Exercise 4: Statement: LM bisects JK Truth Value: True Explanation: We have markers telling us JR ≅ RK. This means JK is being bisected. Exercise 5: Statement: ∠JRP and ∠PRL are complementary. Truth Value: False Explanation: There is no right angle indicator. Exercise 6: Statement: ∠MRQ ≅ ∠PRL Truth Value: True Explanation: These are vertical angles and vertical angles are always congruent.