Question

1 point
Q2. Let R be a relation defined
as : R = {(x,y): y = 2x, x is a
natural number <5}then Range
of R is given as:
O
(a) {2,4,6,8)
O (b) {2,4,6,8,10
)
O (
(C){1,2,3,4)
O (d) N​

Answer 1

Explanation:

We have R = {(x,y) :x ∈ N, y ∈ N, 2x + y = 41}

Domain = {1,2,3,.....,20} {∵ y ∈ N}

∴ R = {(1,39),(2,37),(3,35),....,(19,3),(20,1)}

∴ Range = {1,3,5,....,39}

R is not reflexive as (2,2) ∉ R as 2×2+2≠41

Also, R is not symmetric

as (1,39) ∈ R but (39,1)∉ R

Further, R is not transitive.

as (11,19) ∈ R, (19,3) ∈ R ; but (11,3) ∈ R

Hence, R is neither reflexive nor symmetric and nor transitive.