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The set of ages of Anju's family members is A = 6, 11, 36, 40. What is the cardinal number of the set A? Make a subset by taking any two elements of set A. Is the set A finite or infinite set? Give reason.

Mathematics

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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?
  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 $\boxed{4}$.
    
    • b) Make a subset by taking any two elements of set A.
  2. Choose any two elements from set A.

    For example, 6 and 11.
    A possible subset is 6,11\boxed{{6, 11}}. (Other valid subsets include {6, 36}, {11, 40}, etc.)

    • c) Is the set A finite or infinite set? Give reason.
  3. 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.
  4. 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 $\boxed{{1, 2, 3, 4}}$.
    
    • b) Write whether A and B are the equal or equivalent sets.
  5. 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.
    
  6. 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.
  7. 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.
  8. Find the factors of 6.

    The numbers that divide 6 evenly are 1, 2, 3, and 6.  
    The elements of set M are $\boxed{{1, 2, 3, 6}}$.
    
    • b) Which of the given sets is an infinite set?
  9. 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.
  10. 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.
    
  11. 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<51 \le x < 5}.

    • a) How many subsets of S are possible?
  12. List the elements of set S.

    Square numbers are $1^2=1, 2^2=4, 3^2=9, \dots$.  
    For $1 \le x < 5$, the square numbers are 1 and 4.  
    So, S = {1, 4}.
    
  13. Find the cardinal number of S.

    $n(S) = 2$.
    
  14. Calculate the number of possible subsets using the formula 2n(S)2^{n(S)}.

    Number of subsets $= 2^2 = 4$.  
    There are $\boxed{4}$ possible subsets of S.
    
    • b) Write all possible subsets of S.
  15. List the elements of S

    S = {1, 4}.

  16. List all subsets, including the empty set and the set itself.

    The subsets are $\boxed{\emptyset, \{1\}, \{4\}, \{1, 4\}}$.
    
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