Solve the simultaneous congruences: x = 3 (mod 2) x = 5 (mod 7) (x = 11 (mod 13) The relation R in the set Z on integers given by R={(a,b): a b is divisible by 5} Is a. Reflexive b. Reflexive but not symmetric. c. Symmetric and Transitive. d. Equivalence relation. Which of the following relations is not an equivalence relation on the set of integers. a. x Ry iff xy is an even integer. b. x Ry iff x+y is an even integer. c. x R yiff x = y. d. x Ryiff x ≤y

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.1: Basic Assumptions
Problem 40WE
Question
Solve the simultaneous congruences:
x = 3
(mod 2)
x = 5
(mod 7)
(x = 11
(mod 13)
The relation R in the set Z on integers given by
R={(a,b): a b is divisible by 5}
Is
a. Reflexive
b. Reflexive but not symmetric.
c. Symmetric and Transitive.
d. Equivalence relation.
Which of the following relations is not an equivalence relation on the set of integers.
a. x Ry iff xy is an even integer.
b. x Ry iff x+y is an even integer.
c. x R yiff x = y.
d. x Ryiff x ≤y
Transcribed Image Text:Solve the simultaneous congruences: x = 3 (mod 2) x = 5 (mod 7) (x = 11 (mod 13) The relation R in the set Z on integers given by R={(a,b): a b is divisible by 5} Is a. Reflexive b. Reflexive but not symmetric. c. Symmetric and Transitive. d. Equivalence relation. Which of the following relations is not an equivalence relation on the set of integers. a. x Ry iff xy is an even integer. b. x Ry iff x+y is an even integer. c. x R yiff x = y. d. x Ryiff x ≤y
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