Question

Let R = {a}, S = {x, y} and T = {p, q, r}. Find each of the following sets. a. RX(S XT) b. (RX SXT C. RXSXT 5.

Answer 1

Answer:

Remember that the Cartesian product over n sets X1, ..., Xn is the set

$X_1\times X_2\times\cdots\times X_n=\{(x_1,x_2,\cdots,x_n): x_i \in X_i,\; for\;i=1,\cdots,n\}$

a) First we calculate $S\times T$,

$S\times T=\{(x,p), (x,q),(x,r),(y,p),(y,q),(y,r)\}$

Now, we calculate $R\times(S\times T)$,

$R\times(S\times T)=\{(a,(x,p)), (a,(x,q)), (a,(x,r)), (a,(y,p)),(a,(y,q)),(a,(y,r))\}$

b) We calculate $R\times S\times T$

$R\times S\times T=\{(a,x,p),(a,x,q),(a,x,r),(a,y,p),(a,y,q),(a,y,r)\}$