Question

Determine the Domain and range of the following relations
i) R = {(a, b) / a ∈ N, a < 5, b = 4}
ii) S = {(a, b) / b = |a -1|, a ∈ Z |a| < 3}

Answer 1

i) R = {(a, b) / a ∈ N, a < 5, b = 4}

domain is the set of all elements in which function is defined. and range is the set of all elements which is defined in all elements of domain of function.

here, domain of R = set of all elements of a
e.g., domain(R) $\in\{1,2,3,4\}$

and range of R = set of all elements of b.
e.g., range (R) $\in\{4\}$

ii) S = {(a, b) / b = |a -1|, a ∈ Z |a| < 3}

domain of S = set of all elements of a

here, $|a|<3,a\in\mathbb{Z}$

e.g., $a\in\{-2,-1,0,1,2\}$

so, domain(S) $\in\{-2,-1,0,1,2\}$

range of S = set of all elements of b.

here, b = |a - 1|

so, b = {3, 2, 1, 0}

hence, range (S) $\in\{0,1,2,3\}$

Answer 2

Answer:

Given,

R= {a, b): a N, a < 5, b = 4}

Natural numbers less than 5 are 1, 2, 3 and 4

Therefore, a {1, 2, 3, 4} and b {4}

⇒ R = {(1, 4), (2, 4), (3, 4), (4, 4)}

So,

Domain of relation R = {1, 2, 3, 4}

Range of relation R = {4}