00:01
In this question, we have been asked to find out whether the union of two symmetric relations on a set is symmetric.
00:25
So for this, first let us take two sets.
00:27
Let set r and set s are symmetric, which means that if a, b belongs to set r, then b, a also belongs to set r, which means this is symmetric.
00:49
And if a, b belongs to set s, then b, a also belongs to set s.
00:57
And here we have r is a subset of a x a, subset of a x a and s is a subset of a x a.
01:11
S is a subset of a x a, where r n s is a subset of a x a.
01:22
Now here let a, b belongs to r imply a, b belongs to r x s.
01:33
Let's take this as equation number one.
01:36
Now from this, we can see that a, b belongs to r and a, b belongs to set s.
01:45
Then we have b, a belongs to r and b, a belongs to set s, which means b, a also belongs to r x s...