Question

Let A (0,1,2,3,4,5,6, let B (0,1,2,3,4,5,6,7,8), and let R be the relation from A to B given by "the greatest common divisor of a and b is 2." [Note: "greatest common divisor" is sometimes called "highest common factor"] List the elements of R. t:aph (V,R3 veith pivesn V anel : V p,grs, nll«.sl.lv.sl.lp.sl.lp.s.tp.

Answer 1

Answer:

R = { (2,2), (2, 4), (2, 6), (2,8), (4, 2), (4, 6), (6, 2), (6, 8) }

Step-by-step explanation:

Given,

A = { 0, 1, 2, 3, 4, 5, 6 }

B = { 0,1, 2, 3, 4, 5, 6, 7, 8 }

Also, R is the relation from A to B as follows,

R = { (a, b) : HCF ( a, b ) = 2 ∀ a ∈ A, b ∈ B }

Since,

HCF ( 2, 2 ) = HCF ( 2, 4 ) = HCF ( 2, 6 ) = HCF ( 2, 8 ) = HCF ( 4, 2 ) = HCF ( 4, 6) = HCF ( 6, 4) = HCF ( 6, 2 ) =HCF ( 6, 8 ) = 2

Where, 2, 4, and 6 belong to A,

And, 2, 4, 6 and 8 belong to B,

Hence,

R = { (2,2), (2, 4), (2, 6), (2,8), (4, 2), (4, 6), (6, 2), (6, 4), (6, 8) }