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

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) 289-1 (B) 289-245 (C) 245-1 (D) 290-245

Tardigrade Admin · Accepted Answer

n ( A × A )=100 number of (a,a) type pairs is 10 number of (a, b) and (b, a) type pair of pairs is 45( a ≠ b ) so, required number of relations is 290-245

Q. 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

$2^{89} - 1$

$2^{89} - 2^{45}$

$2^{45} - 1$

$2^{90} - 2^{45}$

$n (A \times A) = 100$
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 $2^{90} - 2^{45}$

Q. 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

289−1

289−245

245−1

290−245