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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?
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.
Choose any two elements from set A.
For example, 6 and 11.
A possible subset is . (Other valid subsets include {6, 36}, {11, 40}, etc.)- c) Is the set A finite or infinite set? Give reason.
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.
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.
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.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.
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.
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?
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.
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.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, }.
- a) How many subsets of S are possible?
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}.Find the cardinal number of S.
$n(S) = 2$.Calculate the number of possible subsets using the formula .
Number of subsets $= 2^2 = 4$. There are $\boxed{4}$ possible subsets of S.- b) Write all possible subsets of S.
List the elements of S
S = {1, 4}.
List all subsets, including the empty set and the set itself.
The subsets are $\boxed{\emptyset, \{1\}, \{4\}, \{1, 4\}}$.
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