Given S =(a,b,c) , T =(b,c,d) and W = (a,d) Find S x T x W
To find the Cartesian product of three sets S, T, and W denoted as S x T x W, you need to combine each element from set S with each element from set T and then with each element from set W.
Let's perform the calculations step by step:
1. Elements from S x T
Combine each element from set S with each element from set T:
S x T = {(a,b,c), (a,c,d), (b,b,c), (b,c,d), (c,b,c), (c,c,d)}
2. Elements from (S x T) x W
Combine each element from the previously obtained set with each element from set W:
(S x T) x W = {((a,b,c),a,d), ((a,c,d),a,d), ((b,b,c),a,d), ((b,c,d),a,d), ((c,b,c),a,d), ((c,c,d),a,d)}
So, the Cartesian product S x T x W is equal to {((a,b,c),a,d), ((a,c,d),a,d), ((b,b,c),a,d), ((b,c,d),a,d), ((c,b,c),a,d), ((c,c,d),a,d)}.