`|(1!,2!,3!),(2!,3!,4!),(3!,4!,5!)|=?`

If A={1,2,3},B={3,4}and C={4,5,6}, "then prove that" (AxxB)uu(AxxC) ={(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5 ),(2,6),(3,3),(3,4),(3,5),(3,6)}

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range: (i) {(2,1), (3,1),(4,2)} (ii) {(2,2),(2,4),(3,3),(4,4)} (iii) {(2,1),(5,1),(8,1),(11,2),(14,2),(17,2)} (iv) {(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} (v){(2,1),(4,2),(6,3),(8,4),(10,5)} (vi) {(1,2),(2,3),(3,4),(3,5),(3,7),(4,8)}

There are three relations R_(1) , R_(2) and R_(3) such that R_(1) = {(2,1),(3,1),(4,2)} , R_(2) = {(2,2),(2,4),(3,3),(4,4)} and R_(3) = {(1,2),(2,3),(3,4),(4,5),(5,6),(6,7)} then

compute the indicated products . (i) [{:(a,b),(-b,a):}][{:(a,-b),(b,a):}](ii) [{:(1),(2),(3):}][2" "3 " "4 ] (iii) [{:(1,-2),(2,3):}][{:(1,2,3),(2,3,1):}] (iv)[{:(2,3,4),(3,4,5),(4,5,6):}][{:(1,-3,5),(0,2,4),(3,0,5):}] (V) [{:(2,1),(3,2),(-1,1):}][{:(1,0,1),(-1,2,1):}] (vi) [{:(3,-1,3),(-1,0,2):}][{:(2,-3),(1,0),(3,1):}]

{:(5,3,7,1),(7,5,9,3),(4,4,4,4),(3,2,?,1):}