Introduction of solution set online:
In the solution set online, a collection of well defined objects is called a set. For example, the collection of all natural numbers, the collection of all equilateral triangles in a plane, the collection of all real numbers, the collection of all vowels in English alphabet are some examples of sets since we can definitely say what objects are there in each of the collections. Consider the following statements for online solution set:
(i) The set of all tall students in your class.
(ii) The set of good books you have studied.
Example of solution set online:
The examples of solution set online is given as follows:
1. If A = {1, 3, 4, 5, 6, 7, 8, 9} and B = {1, 2, 3, 5, 7}, find n(A), n(B), n(AUB) and n(A∩B) and verify the identity
n(AU B) ≡ n(A) +n(B) − n(A∩B).
Solution: We observe that AUB = {1, 2, 3, 4, 5, 6, 7, 8, 9} A∩B ={1, 3, 5, 7}.
n(A) = 8, n(B) = 5, n(A UB) = 9 and n(A∩B) = 4.
We find n(A) + n(B) − n(A∩B) = 8 + 5 − 4 = 9.
Here, n(AUB) = 9. So n(AUB) = n(A) + n(B) − n(A∩B).
In fact, this result is true for any two finite sets.
2. If X = {a, c, d, e, f, g, h, i} and Y = {a, b, c, d, g}, find n(X), n(Y), n(XUY) and n(X∩Y) and verify the identity
n(XU Y) ≡ n(X) +n(Y) − n(X∩Y).
Solution: We observe that XUY = {a, b, c, d, e, f, g, h, i} A∩B ={a, c, e, g}.
n(X) = 8, n(Y) = 5, n(X UY) = 9 and n(X∩Y) = 4.
We find n(X) +n(Y) − n(X∩Y) = 8 + 5 − 4 = 9.
Here, n(XUY) = 9. So n(XUY) = n(X) + n(Y) − n(X∩Y).
In fact, this result is true for any two finite sets. Understanding Subtracting Complex Numbers is always challenging for me but thanks to all math help websites to help me out.
Exercise problems of solution set online:
1. If A = {1, 2, 3} and B = {2, 3, 4}, find A ∩B.
Answer: A∩B = {2, 3}.
The exercise problem of solution set online is given as follow:
2. If A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 7}, find A − B and B − A.
Answer: A−B = {2, 4, 5, 6}. B −A = {7}.
3. If A = {1, 2, 3, 4} and B = {2, 4, 6}, find A UB.
Answer: AUB = {1, 2, 3, 4, 6}.
In the solution set online, a collection of well defined objects is called a set. For example, the collection of all natural numbers, the collection of all equilateral triangles in a plane, the collection of all real numbers, the collection of all vowels in English alphabet are some examples of sets since we can definitely say what objects are there in each of the collections. Consider the following statements for online solution set:
(i) The set of all tall students in your class.
(ii) The set of good books you have studied.
Example of solution set online:
The examples of solution set online is given as follows:
1. If A = {1, 3, 4, 5, 6, 7, 8, 9} and B = {1, 2, 3, 5, 7}, find n(A), n(B), n(AUB) and n(A∩B) and verify the identity
n(AU B) ≡ n(A) +n(B) − n(A∩B).
Solution: We observe that AUB = {1, 2, 3, 4, 5, 6, 7, 8, 9} A∩B ={1, 3, 5, 7}.
n(A) = 8, n(B) = 5, n(A UB) = 9 and n(A∩B) = 4.
We find n(A) + n(B) − n(A∩B) = 8 + 5 − 4 = 9.
Here, n(AUB) = 9. So n(AUB) = n(A) + n(B) − n(A∩B).
In fact, this result is true for any two finite sets.
2. If X = {a, c, d, e, f, g, h, i} and Y = {a, b, c, d, g}, find n(X), n(Y), n(XUY) and n(X∩Y) and verify the identity
n(XU Y) ≡ n(X) +n(Y) − n(X∩Y).
Solution: We observe that XUY = {a, b, c, d, e, f, g, h, i} A∩B ={a, c, e, g}.
n(X) = 8, n(Y) = 5, n(X UY) = 9 and n(X∩Y) = 4.
We find n(X) +n(Y) − n(X∩Y) = 8 + 5 − 4 = 9.
Here, n(XUY) = 9. So n(XUY) = n(X) + n(Y) − n(X∩Y).
In fact, this result is true for any two finite sets. Understanding Subtracting Complex Numbers is always challenging for me but thanks to all math help websites to help me out.
Exercise problems of solution set online:
1. If A = {1, 2, 3} and B = {2, 3, 4}, find A ∩B.
Answer: A∩B = {2, 3}.
The exercise problem of solution set online is given as follow:
2. If A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 7}, find A − B and B − A.
Answer: A−B = {2, 4, 5, 6}. B −A = {7}.
3. If A = {1, 2, 3, 4} and B = {2, 4, 6}, find A UB.
Answer: AUB = {1, 2, 3, 4, 6}.
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