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1 0 f Converse tfrwsnyttareparal ~u#sntne
2
3 * Types of statements: Conditional Converse Biconditional Negation - If. - I then statement - Statement in which the If and then are switched - when a conditional and its inverse are both true then they can be written together " " if and only if using * Inverse
4 Evaluate the truth value of the _ statement: Bellefonte is the capital of Pennsylvania FALSE Write the statement's negation, changing Truth Its = = value Negation: Bellefonte is not the capital of Pennsylvania
5 L MLXYZ Today is Tuesday LABC is not obtuse lines M and n are perpendicular Mtn
6 Inverse of a conditional statement - Etienne your bafwhpnaoyhob both the hypothesis and are January 29, 2018 prepared conclusion are negated. f- If you then do not have your you are not backpack prepared
7 If g hypothesis Then, g January 29, 2018 conclusion Contrapositive of a conditional statement youhaf.tn yfparc.fi and hypothesis conclusion are switched and both negated F@ If are not you prepared, don't have then you backpack your
8 - Conditional Statement: - If a figure is a square, then it is a rectangle. TR Tr@,) * Converse: If a figure is a rectangle squanett.tt# Then it is a square. Inverse: is not a figure FALSE Then it is not a rectangle. Contrapositive: If figure a is not a Then it is not a square. Evaluate the truth values of the statements
9 If d hyp. 61 then they never intersect =, Conclusion. two-way inverse : If 2 lines are not parallel then they Cypher do If 2 lines do intersect intersected they are not
10 Conditional: Converse: Inverse: Contrapositive:
11 Equivalent Statements statements are that same atwraoysnhayagoteu ( refer to the same objects ) ) A conditional statement and its Contra positive are equivalent statements ran
12 - s
13 Proofs Using Indirect Reasoning consider all possibilities, then Prove all one to be false except The remaining possibility must be true How to use indirect reasoning: To prove is true - that a State meet assume its negation then shhow that is false -
14 . January 29, 2018 Steps to writing an indirect proof Step 1: State as an opposite C negation ) of what you to prove Step 2: Show this leads assumption to a contradiction Step 3: Conclude that the assumption Must be false therefore what you want to prove is the true want
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16 The : Quad. QRWX does have four acute angles. since acute angles are < 90 the sum of 4 acute < s is < 3600 but this contradicts the fact that the sum of angles in a Quad = 360. Assume : An integer n is Not divisible by 5. ' Therefore the is assumptions FALSE Assay : MLAEMLB
17 -0 - I # 0 0
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19 of Indio f January 29, x Assume : LAELB a then ATEBT by Th. 4-4 this So AC=BC by that def. contradict the BCSAC So the is assumption therefore LA LB I seq. Given FALSE
20 w/ base angles and January 29, 2018
21 Given : - OABC w/rt. LC MLC = 90 - Prove : MLA Assume MLA #. 90 < 90. Since mlc= 90 MLATMLC 2180 this can't be true since if it equals 180 then MLB would = 0 and if > 180 this wouldn't be a so the assumptions is false by Th, 12 therefore MLAC 90
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23 Two angles are not congruent January 29, 2018
24 a. If a figure is not a rectangle, then it doesn't have four sides b. If a figure doesn't have four sides, then it is not a rectangle.
25 Assume that Triangle PEN is not isosceles January 29, 2018
26 I and II since a right triangle can't be equilateral I and II since it must be a right triangle if A and C are both 60 degrees, B can't be a right angle.
27 a. 20 or more members b. Total membership is fewer than 20 c. The Debate Club has few than 10 members.
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30 a. if four points are not collinear, then they are not coplanar - FALSE - see points above b. if four points are not coplanar, then they are not collinear - TRUE
31 27) If a student attends school in the Fairmont building, then she has Jon Downs as a school director. Inverse: If a student doesn't attend school in the Fairmont Building, then she doesn't have Jon Downs as a school director s 28. Not possible. If the conditional statement is true, the contrapositive will always have the same truth value, so it would also have to be true.
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