solve it a) Identify which of these relations are reflexive, which are symmetric, which aretransitive,and which are equivalence relations. You do not need to show any working.{(a, b) | a is the same species as b} Ci) A is the set of all animals, R1Ax Aii) R2 = {(m, n) | m² < n?} CZx Zii) R3 = {(x, y) |r +y < 1} CR x R%3Div) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2, 2)}CBx Bv) B = {0, 1, 2}, R, = {(0, 1), (1, 2), (2,0)} C Bx B

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a) Identify which of these relations are reflexive, which are symmetric, which are transitive, and which are equivalence relations. You do not need to show any working. i) A is the set of all animals, R1 Ax A {(a, b) | a is the same species as b} C %3D i) R2 = {(m, n) | m² < n?} CZx Z ii) R3 = {(x, y) | r+ y < 1} CR xR iv) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2,2)} CBx B v) B = {0, 1, 2}, R5 = {(0, 1), (1, 2), (2,0)} CBx B

a) Identify which of these relations are reflexive, which are symmetric, which are transitive, and which are equivalence relations. You do not need to show any working. i) A is the set of all animals, R1 Ax A {(a, b) | a is the same species as b} C %3D i) R2 = {(m, n) | m² < n?} CZx Z ii) R3 = {(x, y) | r+ y < 1} CR xR iv) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2,2)} CBx B v) B = {0, 1, 2}, R5 = {(0, 1), (1, 2), (2,0)} CBx B

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

solve it

a) Identify which of these relations are reflexive, which are symmetric, which are
transitive,
and which are equivalence relations. You do not need to show any working.
{(a, b) | a is the same species as b} C
i) A is the set of all animals, R1
Ax A
ii) R2 = {(m, n) | m² < n?} CZx Z
ii) R3 = {(x, y) |r +y < 1} CR x R
%3D
iv) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2, 2)}CBx B
v) B = {0, 1, 2}, R, = {(0, 1), (1, 2), (2,0)} C Bx B

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