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. The set A is defined as A = \x N: 13 < x < 17 এবং x মৌলিক সংখ্যা\. This means x must be a natural number greater than 13 and less than 17, and x must be a prime number. The natural numbers between 13 and 17 are 14, 15, 16. • 14 is not a prime number (14 = 2 × 7). • 15 is not a prime number (15 = 3 × 5). • 16 is not a prime number (16 = 2 × 8). Since there are no prime numbers between 13 and 17, the set A is an empty set. A = \\ Step 2: Determine the number of elements in set A. The number of elements in A, denoted as |A|, is 0. |A| = 0 Step 3: Calculate the number of elements in the power set of A. The number of elements in the power set of a set with n elements is given by the formula 2^n. In this case, n = |A| = 0. So, the number of elements in the power set of A, denoted as |P(A)|, is 2^0. |P(A)| = 2^0 = 1 Step 4: Select the correct option. The calculated number of elements in P(A) is 1. Comparing this with the given options: ক) 0 খ) 1 গ) 4 ঘ) 8 The correct option is খ). The number of elements in P(A) is 1.