The number of symmetric relations defined on the set {1,2,3,4} which are not reflexive is________.

To solve this problem, we need to understand a few concepts:

1. Symmetric Relation: A relation R on a set A is said to be symmetric if (a, b) ∈ R implies (b, a) ∈ R for all a, b ∈ A.

2. Reflexive Relation: A relation R on a set A is said to be reflexive if (a, a) ∈ R for every a ∈ A.

3. The total number of relations on a set with n elements is 2^(n^2).

Now, let's solve the problem:

The set given is {1,2,3,4}, so n=4.

The total number of relations on this set is 2^(4^2) = 2^16.

The total number of symmetric relations on this set is 2^(n(n+1)/2) = 2^(4*5/2) = 2^10.

However, we are asked to find the number of symmetric relations that are not reflexive.

A reflexive relation must include all pairs (a, a), so there are 4 such pairs in this set.

The number of symmetric relations that include these pairs is 2^(n(n-1)/2) = 2^(4*3/2) = 2^6.

So, the number of symmetric relations that are not reflexive is 2^10 - 2^6 = 1024 - 64 = 960.