DISCRETE MATHEMATICS LOOSELEAF W/CONNECT

8th Edition

ISBN: 9781264309405

Author: ROSEN

Publisher: MCG

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Textbook Question

Chapter 9.1, Problem 39E

d the relationsS²fori= 1, 2, 3,4, , 6i’here

S 1 = { ( a , b ) ∈ Z 2 | a > b } ,the greater than relation,

S 2 = { ( a , b ) ∈ Z 2 | a ≥ b } ,the greater than or equal to relation,

S 3 = { ( a , b ) ∈ Z 2 | a < b } ,the less than relation,

S 4 = { ( a , b ) ∈ Z 2 | a ≤ b } ,the less than or equal to relation,

S 5 = { ( a , b ) ∈ Z 2 | a = b } ,the equal to relation,

S 6 = { ( a , b ) ∈ Z 2 | a ≠ b } ,the unequal to relation.

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Chapter 9.1, Problem 38E

Chapter 9.1, Problem 40E

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Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.

Chapter 9 Solutions

DISCRETE MATHEMATICS LOOSELEAF W/CONNECT

Ch. 9.1 - t the ordered pairs in the...Ch. 9.1 - a) List all the ordered pairs in the relation R =...Ch. 9.1 - each of these relations on the set {1, 2, 3, 4},...Ch. 9.1 - ermine whether the relationRon the set of all...Ch. 9.1 - ermine whether the relationRon the set of all Web...Ch. 9.1 - ermine whether the relationRon the set of all real...Ch. 9.1 - ermine whether the relationRon the set of all...Ch. 9.1 - w that the relationR=Oon a nonempty set S is...Ch. 9.1 - Show that the relationR=on the empty setS=is...Ch. 9.1 - e an example of a relation on a set that is a)...

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Solution Summary: The author explains the relation R_i2 for I=1,2,

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