Question

let A={x:x €N, x<11} and R be a relation from A to A defined by R={(a,b) : |a-b| is multiple of 4 } find the set of all elements to 2.

Answer 1

the number of devices is a

Answer 2

Here, we are given that set $A = \{x: x \in N, x<11 \}$

It means that A can have values from 1 to 10 or we can say $[1,11)$ i.e. 1 inclusive and 11 is not inclusive.

According to set A, if we look at relation R:

$R = \{(a,b) : |a-b| \text{ is a multiple of 4} \}$

The following values can be possible here, that satisfy that above condition of Relation :

$R = \{(1,5), (1,9), (2,6), (2,10), (3,7), (4,8), (5,1),(5,9),(6,2),\\(6,10),(7,3),(8,4),(9,1),(9,5),(10,2), (10,6)\\(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(8,8),(9,9),(10,10)\}$

$0$ is a multiple of every number so elements like $(1,1), (2,2) ..... (10,10)$ are members of above relation.

Hence, the above is relation $R$.