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.
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Here are the solutions to the problems from the image. 1. The set of ages of Anju's family members is A = 6, 11, 36, 40. a) What is the cardinal number of the set A? Step 1: Count the number of distinct elements in set A. The elements are 6, 11, 36, 40. There are 4 distinct elements. The cardinal number of set A is 4. b) Make a subset by taking any two elements of set A. Step 1: Choose any two elements from set A. For example, 6 and 11. A possible subset is 6, 11. (Other valid subsets include 6, 36, 11, 40, etc.) c) Is the set A finite or infinite set? Give reason. Step 1: Determine if the number of elements is countable. Set A has 4 elements, which is a countable number. Set A is a finite set because it has a definite and countable number of elements. 2. Two given sets are A = 2, 4, 6, 8 and B = x: x is a natural number less than 5. a) List the elements of the set B. Step 1: Identify natural numbers less than 5. Natural numbers are positive integers starting from 1. So, numbers less than 5 are 1, 2, 3, 4. The elements of set B are 1, 2, 3, 4. b) Write whether A and B are the equal or equivalent sets. Step 1: Compare the elements of A and B. A = 2, 4, 6, 8 and B = 1, 2, 3, 4. The elements are not exactly the same, so they are not equal sets. Step 2: Compare the cardinal numbers of A and B. Cardinal number of A, n(A) = 4. Cardinal number of B, n(B) = 4. Since n(A) = n(B), sets A and B are equivalent sets. c) Are the sets A and B disjoint or overlapping? Give reason. Step 1: Check for common elements between A and B. A = 2, 4, 6, 8 and B = 1, 2, 3, 4. The common elements are 2 and 4. Since they have common elements, sets A and B are overlapping sets. 3. Three given sets are L = 2, 3, 5, 7, M = factors of 6 and N = 1, 2, 3, .... a) List the elements of set M. Step 1: Find the factors of 6. The numbers that divide 6 evenly are 1, 2, 3, and 6. The elements of set M are 1, 2, 3, 6. b) Which of the given sets is an infinite set? Step 1: Examine each set for countability. L = 2, 3, 5, 7 has 4 elements (finite). M = 1, 2, 3, 6 has 4 elements (finite). N = 1, 2, 3, ... indicates that the numbers continue indefinitely (uncountable). Set N is an infinite set. c) State with reason whether the sets L and M are equal or equivalent sets. Step 1: Compare the elements of L and M. L = 2, 3, 5, 7 and M = 1, 2, 3, 6. The elements are not exactly the same, so they are not equal sets. Step 2: Compare the cardinal numbers of L and M. Cardinal number of L, n(L) = 4. Cardinal number of M, n(M) = 4. Since n(L) = n(M), sets L and M are equivalent sets. 4. A given set is S = x: x is square number, 1 x < 5. a) How many subsets of S are possible? Step 1: List the elements of set S. Square numbers are 1^2=1, 2^2=4, 3^2=9, . For 1 x < 5, the square numbers are 1 and 4. So, S = 1, 4. Step 2: Find the cardinal number of S. n(S) = 2. Step 3: Calculate the number of possible subsets using the formula 2^n(S). Number of subsets = 2^2 = 4. There are 4 possible subsets of S. b) Write all possible subsets of S. Step 1: List the elements of S: S = 1, 4. Step 2: List all subsets, including the empty set and the set itself. The subsets are , \1\, \4\, \1, 4\. Last free one today — make it count tomorrow, or type /upgrade for unlimited.