Question

What is the Cartesian product of {a,b,c} and {x,y,z}? Group of answer choices A.{(a,x),(b,y),(c,z)} B.{(a,x),(b,x),(c,x),(a,y),(b,y),(c,y),(a,z),(b,z),(c,z)} C. {(a,b,c),(x,y,z)} D. {(a,x,y,z),(b,x,y,z),(c,x,y,z)}

Answer 1

The Cartesian product of {a,b,c} and {x,y,z} is all the possible ordered pairs of elements from the first set with elements from the second set, resulting in option B: {(a,x), (a,y), (a,z), (b,x), (b,y), (b,z), (c,x), (c,y), (c,z)}.

Step-by-step explanation:

The Cartesian product of two sets A and B, denoted by A×B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In the case of the sets {a,b,c} and {x,y,z}, the Cartesian product would include every combination of elements from the first set with elements from the second set.

Therefore, the Cartesian product of {a,b,c} and {x,y,z} is {(a,x), (a,y), (a,z), (b,x), (b,y), (b,z), (c,x), (c,y), (c,z)}. This corresponds to option B. Each element of the first set is paired with each element of the second set, resulting in 3×3 = 9 ordered pairs.