Question

Show that the relation R in the set ℝ of real numbers defined as R={(a, b): a,b∈ ℝ and a≤ 3} is neither
reflexive, nor symmetric nor transitive

plss answer it anyone relation and function class 12

Answer 1

Answer:

R={(a−b):a≤b

3

}

(i) since (a,a)∈

/

R as a≤a

3

is not always true

[Take a = 1/3. then a≤a

3

is not true]

∴R is not reflexive

(ii) Also(a,b)ϵR⇒(b,a)ϵR

[Take a = 1, b=4, ∴1≤4

3

but 4(1)

3

]

∴ R is not symmetric

(iii) Now (a,b)ϵR(b,c)ϵR⇒(a,c)∴R

[Take a=100,b=5,c=3,∴100≤5

3

,5≤3

3

but 100≥3

3

]

R is not symmetric.

Answer 2

Answer:

R = { (a - b):a≤ b3 } (i) since (a,a) ∉ R as a≤ a3 is not always true[Take a = 1/3. then a≤ a3 is not true] R is not reflexive(ii) Also (a,b)ϵ