Question

Let $A$ be a non-empty set such that $A\times A$ has $16$ elements among which three elements are found to be $(a,b),(b,c)$ and $(c,d)$ and $I_A$ be the identity relation on $A,$ then

• A. $A=\{a,b,c\}$
• B. $I_A=\left\{\right(a,a),(b,b),(c,c\left)\right\}$
• C. $A=\{a,b,c,d\}$
• D. $I_A=\left\{\right(a,a),(b,b),(c,c),(d,d\left)\right\}$

Answer 1

Answer: (C), (D)

$I_A=\left\{\right(a,a),(b,b),(c,c),(d,d\left)\right\}$

$n(A\times A)=16$
$\Rightarrow n\left(A\right)=4$
$\Rightarrow A=\{a,b,c,d\}$
$\Rightarrow I_A=\left\{\right(a,a),(b,b),(c,c),(d,d\left)\right\}$