Question

Let $A$ be a set consisting of $10$ elements. The number of non-empty relations from $A$ to $A$ that are reflexive but not symmetric is

• A. $2^{89}-1$
• B. $2^{89}-2^{45}$
• C. $2^{45}-1$
• D. $2^{90}-2^{45}$

Answer 1

Answer: (D)

$n ( A \times A )=100$
number of (a,a) type pairs is 10
number of $(a, b)$ and $(b, a)$ type pair of pairs is
$45( a \neq b )$
so, required number of relations is $2^{90}-2^{45}$