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### High School Mathematics8.1 Cartesian Product of Sets

 If A and B are any two sets, the set of all possible ordered pairs (a,b) with a Î A and b Î B, is called the cartesian product of A and B and is denoted by A ´ B. and it is read as A cross B. The set builder form of A ´ B is A ´ B = {(a,b)/a Î A and b Î B} Observing the above relation we find the following points. 1. The ordered pair of A ´ B, the first coordinate belongs to A while the second coordinate belongs to B. 2. A ´ B ¹ B ´ A. 3. If n(A)= a and n(B) = b then n(A ´ B) = ab. 4. If A is empty or B is empty then A ´ B is empty. 5. If one of the sets A and B is infinite the other is non-empty then A ´ B is also infinite. Example: If A = {1,3,5} and B = {2,4}, then find A´ B and B ´ A and also find n(A ´ B). Solution: (i). A ´ B = {1,3,5} ´ {2,4} = {(1,2),(1,4),(3,2),(3,4),(5,2),(5,4)} (ii). B ´ A = {2,4} ´ {1,3,5} = {(2,1),(2,3),(2,5),(4,1),(4,3),(4,5)} (iii). n(A ´ B) = n(A) * n(B) Where n(A) and n(B) are the number of elements in the set A and B respectively. n(A ´ B) = 3 * 2 = 6 Directions: Choose the correct answer. Also write at least 5 examples of your own.
 Q 1: If A = {2,4,6} and B = {1,3} then find B ´ A.{(1,2),(1,4),(1,6),(3,1),(3,4),(3,6)}{(1,3),(1,4),(1,6),(3,2),(3,4),(3,6)}{(1,2),(1,4),(1,6),(3,2),(3,1),(3,6)}{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6)} Q 2: If A = {2,3,4} and B = {5,6} then find n(A ´ B).28262425 Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!

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