This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Determine the elements of set A. Set A is the set of even natural numbers less than 8. The natural numbers are \1, 2, 3, \. The even natural numbers less than 8 are \2, 4, 6\. So, A = \2, 4, 6\. The number of elements in set A is n(A) = 3. Step 2: Determine the elements of set B. Set B is the set of prime numbers less than 7. The prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers less than 7 are \2, 3, 5\. So, B = \2, 3, 5\. The number of elements in set B is n(B) = 3. Step 3: Calculate the number of elements in the Cartesian product A × B. The number of elements in A × B is given by the product of the number of elements in A and the number of elements in B. n(A × B) = n(A) × n(B) n(A × B) = 3 × 3 = 9 Step 4: Calculate the number of relations from A to B. A relation from set A to set B is any subset of A × B. If a set has m elements, then the number of its subsets is 2^m. Since A × B has 9 elements, the total number of possible relations from A to B is 2^n(A × B). Number of relations = 2^9 Step 5: Select the correct option. The calculated number of relations is 2^9, which corresponds to option (A). The final answer is A 3 done, 2 left today. You're making progress.