Answer:
Remember that the Cartesian product over n sets X1, ..., Xn is the set
[tex]X_1\times X_2\times\cdots\times X_n=\{(x_1,x_2,\cdots,x_n): x_i \in X_i,\; for\;i=1,\cdots,n\}[/tex]
a) First we calculate [tex]S\times T[/tex],
[tex]S\times T=\{(x,p), (x,q),(x,r),(y,p),(y,q),(y,r)\}[/tex]
Now, we calculate [tex]R\times(S\times T)[/tex],
[tex]R\times(S\times T)=\{(a,(x,p)), (a,(x,q)), (a,(x,r)), (a,(y,p)),(a,(y,q)),(a,(y,r))\}[/tex]
b) We calculate [tex]R\times S\times T[/tex]
[tex]R\times S\times T=\{(a,x,p),(a,x,q),(a,x,r),(a,y,p),(a,y,q),(a,y,r)\}[/tex]
