Get the complete, step-by-step math solution for: "If {P}=\{1{,}2\}, form the set {P} × {P} × {P}.". Powered by SolveForX AI math tutor.
Step 1: Understand the Cartesian Product
The Cartesian product of two sets A and B, denoted as A×B, is the set of all possible ordered pairs (a,b) where a is an element of A and b is an element of B. For three sets, A×B×C is the set of all ordered triplets (a,b,c) where a∈A, b∈B, and c∈C.
Step 3: Calculate P × P
First, let's find the Cartesian product of P with itself. This involves forming all possible ordered pairs where both elements come from P. The elements are (1,1), (1,2), (2,1), and (2,2).
Step 5: List all elements of P × P × P
By combining each pair from P×P with each element from P, we get the following ordered triplets: (1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), and (2,2,2). There are 2×2×2=8 elements in total.