R1 = {(a, b) ∈ R2 ∣ a > b}, the greater than relation, R2 = {(a, b) ∈ R2 ∣ a ≥ b}, the greater than or equal to relation, R3 = {(a, b) ∈ R2 ∣ a < b}, the less than relation, R4 = {(a, b) ∈ R2 ∣ a ≤ b}, the less than or equal to relation, R5 = {(a, b) ∈ R2 ∣ a = b}, the equal to relation, R6 = {(a, b) ∈ R2 ∣ a ≠ b}, the unequal to relation. Find a) R1 ∪ R3. b) R1 ∪ R5. c) R2 ∩ R4.
R1 = {(a, b) ∈ R2 ∣ a > b}, the greater than relation, R2 = {(a, b) ∈ R2 ∣ a ≥ b}, the greater than or equal to relation, R3 = {(a, b) ∈ R2 ∣ a < b}, the less than relation, R4 = {(a, b) ∈ R2 ∣ a ≤ b}, the less than or equal to relation, R5 = {(a, b) ∈ R2 ∣ a = b}, the equal to relation, R6 = {(a, b) ∈ R2 ∣ a ≠ b}, the unequal to relation. Find a) R1 ∪ R3. b) R1 ∪ R5. c) R2 ∩ R4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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R1 = {(a, b) ∈ R2 ∣ a > b}, the greater than relation,
R2 = {(a, b) ∈ R2 ∣ a ≥ b}, the greater than or equal to
relation,
R3 = {(a, b) ∈ R2 ∣ a < b}, the less than relation,
R4 = {(a, b) ∈ R2 ∣ a ≤ b}, the less than or equal to
relation,
R5 = {(a, b) ∈ R2 ∣ a = b}, the equal to relation,
R6 = {(a, b) ∈ R2 ∣ a ≠ b}, the unequal to relation.
Find
a) R1 ∪ R3.
b) R1 ∪ R5.
c) R2 ∩ R4.
d) R3 ∩ R5.
e) R1 − R2.
f ) R2 − R1.
g) R1 ⊕ R3.
h) R2 ⊕ R4.
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