Consider these relations on the set of real numbers R1 a b

Consider these relations on the set of real numbers:

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 |ab},the“lessthanorequalto” relation,

R5 ={(a,b)R2 |a=b},the“equalto”relation,

R6 = {(a, b) R2 | a = b}, the “unequal to” relation.

Find: 9.1 34-36

R1 U R3

R2 R4.

R2 R1

R3R₅

R4 R6

R1R2

R1R6

R2R3

my answers

R1 denotes the region in two-dimensional plane above the line y = x

R2 denotes the region in two-dimensional plane above the line y = x and including the line y = x

R3 denotes the region in two-dimensional plane below the line y = x

R4 denotes the region in two-dimensional plane below the line y = x and including the line y = x

R5 denotes the region in two-dimensional plane as the line y = x

R6 denotes the region in two-dimensional plane above and below the line y = x but not including y = x

R1 U R3 = Region above and below y = x => R6

R2 R4 = Region overlapping between above y = x with y = x and below y = x with y = x => R5

R2 - R1 = Region which in excess as above y = x => R5

R3 R5 = Region formed by below y = x with the line y = x => R4

R4 R6 = Region of line y = x is removed from R4 => R3

R1 R2 = Region common to above y = x and above y = x and including y = x => R1

R1 R6 = Region common to where y is not equal to x and y is greater than x => R1

R2 R3 = Region overlapping for y x and y < x => Null Set