Question

For any relation $R$ between the two sets $A,B$ given as:
$R=\left\{\right(1,1),(2,4),(3,9),(4,16\left)\right\}.$ Select the set builder representation of the given relation.

• A. $R=\left\{\right(a,b):a\in A,b\in B,b=a^3\}$
• B. $R=\left\{\right(a,b):a\in A,b\in B,b=2a^2\}$
• C. $R=\left\{\right(a,b):a\in A,b\in B,b=a^2\}$
• D. $R=\left\{\right(a,b):a\in A,b\in B,b=a\}$

Answer 1

The correct option is C $R=\left\{\right(a,b):a\in A,b\in B,b=a^2\}$

Given the relation between the sets $A\&B$ as:
$R=\left\{\right(1,1),(2,4),(3,9),(4,16\left)\right\}$
Clearly, the second term is the square of the first term in the given relation:
Thus, the relation:
$R=\left\{\right(a,b):a\in A,b\in B,b=a^2\}$ is the correct set builder representation of the given relation.