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
2. c) Set C = Even numbers less than 15 Step 1: Identify even numbers within the universal set = \1, 2, ..., 20\ that are less than 15. The numbers in less than 15 are \1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\. Step 2: From this list, select the even numbers. Set C is \2, 4, 6, 8, 10, 12, 14\. 2. d) A C Step 1: Recall Set A and Set C. Set A = \3, 6, 9, 12, 15, 18\ Set C = \2, 4, 6, 8, 10, 12, 14\ Step 2: Find the common elements between Set A and Set C. The elements present in both sets are 6 and 12. A C = \6, 12\. 2. e) B C Step 1: Recall Set B and Set C. Set B = \7, 9, 11, 13, 15, 17, 19\ Set C = \2, 4, 6, 8, 10, 12, 14\ Step 2: Find the common elements between Set B and Set C. There are no common elements between these two sets. B C = \\ (or ). 2. f) A B C Step 1: Find the intersection of Set A, Set B, and Set C. We know that B C = \\. Step 2: The intersection of any set with an empty set is an empty set. A B C = A (B C) = A \\ = \\ (or ). 2. g) A C Step 1: Recall Set A and Set C. Set A = \3, 6, 9, 12, 15, 18\ Set C = \2, 4, 6, 8, 10, 12, 14\ Step 2: Combine all unique elements from both sets. A C = \2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 18\. 3. a) Find the L.C.M of 8, 12 and 18 Step 1: Find the prime factorization of each number. 8 = 2 × 2 × 2 = 2^3 12 = 2 × 2 × 3 = 2^2 × 3^1 18 = 2 × 3 × 3 = 2^1 × 3^2 Step 2: Identify the highest power for each prime factor present in any of the numbers. The prime factors are 2 and 3. Highest power of 2 is 2^3. Highest power of 3 is 3^2. Step 3: Multiply these highest powers to find the L.C.M. L.C.M = 2^3 × 3^2 = 8 × 9 = 72 The L.C.M of 8, 12, and 18 is 72. 3. b) Find the H.C.F of 36, 48 and 60 Step 1: Find the prime factorization of each number. 36 = 2 × 2 × 3 × 3 = 2^2 × 3^2 48 = 2 × 2 × 2 × 2 × 3 = 2^4 × 3^1 60 = 2 × 2 × 3 × 5 = 2^2 × 3^1 × 5^1 Step 2: Identify the lowest power for each common prime factor present in all numbers. The common prime factors are 2 and 3. Lowest power of 2 is 2^2. Lowest power of 3 is 3^1. Step 3: Multiply these lowest powers to find the H.C.F. H.C.F = 2^2 × 3^1 = 4 × 3 = 12 The H.C.F of 36, 48, and 60 is 12. That's 2 down. 3 left today — send the next one.