if relation r1 and r2 from set A to set B are defined as r1{(1,2),(3,4),(5,6)} and r2 ={(2,1),(4,3),(6,5)}, then n(AXB)
Options
A)35
B)91
C)53
D)55
Are you sure ??
I mean is something wrong in statement
You got me. A and B appear to be sets, and r1 and r2 take A→B
but usually in set notation, AxB is the set of all ordered pairs (a,b) where a∈A and b∈B.
So defining r1 and r2 doesn't seem to me to have anything to do with AxB
To find the number of elements in the Cartesian product of sets A and B, denoted as AxB, you need to multiply the number of elements in set A by the number of elements in set B.
In this case, set A has three elements (1, 3, 5) and set B also has three elements (2, 4, 6). So, the number of elements in AxB is 3 * 3 = 9.
However, the sets A and B are not given directly. Instead, relation r1 is given as a set of ordered pairs (1,2), (3,4), and (5,6), and relation r2 is given as a set of ordered pairs (2,1), (4,3), and (6,5).
To find the sets A and B, you need to look at the elements in the ordered pairs. In this case, the elements in A are the first elements in each ordered pair, and the elements in B are the second elements in each ordered pair.
For relation r1:
Set A = {1, 3, 5}
Set B = {2, 4, 6}
For relation r2:
Set A = {2, 4, 6}
Set B = {1, 3, 5}
Since both r1 and r2 have the same sets A and B, it doesn't matter which relation you use to find AxB. Using either relation, the sets A and B are the same, so the number of elements in AxB is 3 * 3 = 9.
Therefore, the correct option is:
B) 91
It appears that A = B = {1,2,3,4,5,6}
So n(AxB) = n(A) * n(B) = 6*6 = 36
Not sure what r1 and r2 have to do with it.