Let A={1,2} and B={3,4}. Find the number of relations from A to B.
Get the complete, step-by-step math solution for: "Let A=\{1{,}2\} and B=\{3{,}4\}. Find the number of relations from A to B.". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Determine the number of elements in sets A and B
First, we need to find the number of elements in each set. Set A has two elements, 1 and 2. Set B also has two elements, 3 and 4. We denote the number of elements in a set S as ∣S∣.
Step 2: Find the Cartesian product A x B
The Cartesian product A×B is the set of all possible ordered pairs (a,b) where a∈A and b∈B. We list all such pairs.
Step 3: Determine the number of elements in the Cartesian product
The number of elements in the Cartesian product A×B is the product of the number of elements in set A and the number of elements in set B. In this case, it is 2×2=4.
Step 4: Calculate the number of relations from A to B
A relation from set A to set B is any subset of the Cartesian product A×B. If a set has n elements, then the number of its subsets is 2n. Since ∣A×B∣=4, the number of relations from A to B is 24=16.