Question

Let A 10,1,2,3,4,5,61, let B 0,1,2,3,4,5,6,7,81, 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.

Answer 1

R={(10,2),(10,4),(10,6),(2,2),(2,4),(2,6),(4,2),(4,6)}

Explanation:

We are given that

A={10,1,2,3,4,5,61}

B={0,1,2,3,4,5,6,7,81}

We are given that R be the relation from A to B

R={gcd(a,b)=2,a
`\inA,b\inB`}

Gcd=Greatest common divisor of a and b.

We have to find the elements in R

(10,2)=2,(10,4)=2,(10,6)=2

(2,2)=2,(2,4)=2,(2,6)=2

(4,2)=2,(4,6)=2

Therefore, R={(10,2),(10,4),(10,6),(2,2),(2,4),(2,6),(4,2),(4,6)}