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Introduction to solution set solving online: In mathematics, to solution set solving online is to find what values (numbers, functions, sets, etc.) satisfy a condition stated in the form of an equation (two expressions related by equality). In solution set the expressions includes one or more unknowns, which are free variables for which values are sought that cause the condition to be fulfilled. To be particularly, what is required are frequently not necessarily actual values, but, more in general, mathematical expressions. A solution set of the equation is an assignment of expressions to the unknowns that satisfies the equation by solving online; in other words, expressions such that, when they are substituted for the unknowns, the equation becomes a tautology (a provably true statement). (source from wikipedia) Examples for solution set solving online Description: A group of items is called a set. For example, the group of all natural numbers, the group of all equilateral triangles in a plane, the collection of all real numbers, the collection of all vowels in alphabets is some examples of sets. Online solution is very easy one..We can solve the set by online solution. The following two value statements are used to represents for 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(AnB) and verify the identity n(AU B) = n(A) +n(B) - n(AnB). Solution: We observe that AUB = {1, 2, 3, 4, 5, 6, 7, 8, 9} AnB ={1, 3, 5, 7}. n(A) = 8, n(B) = 5, n(A UB) = 9 and n(AnB) = 4. We find n(A) + n(B) - n(AnB) = 8 + 5 - 4 = 9. Here, n(AUB) = 9. So n(AUB) = n(A) + n(B) - n(AnB). 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(XnY) and verify the identity n(XU Y) = n(X) +n(Y) - n(XnY). Solution: We observe that XUY = {a, b, c, d, e, f, g, h, i} AnB ={a, c, e, g}. n(X) = 8, n(Y) = 5, n(X UY) = 9 and n(XnY) = 4. We find n(X) +n(Y) - n(XnY) = 8 + 5 - 4 = 9. Here, n(XUY) = 9. So n(XUY) = n(X) + n(Y) - n(XnY). In fact, this result is true for any two finite sets. Exercise problems of solution set online: 1. If A = {1, 2, 3} and B = {2, 3, 4}, find A nB. Answer: AnB = {2, 3}. 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}. Example of solution set online: Practice problems: 1. If M = {1, 3, 4, 5} and N= {1, 2, 3}, Solving online for the soution set, n(M), n(N), n(MUN) and n(MnN) Solution: We note that MUN = {1, 2, 3, 4, 5} MnN ={1, 3}. n(M) = 4, n(N) = 3, n(MUN) = 5 and n(MnN) = 2. We can find n(M) + n(N) - n(MnN) = 4 + 3 - 2 = 5 Here, n(MUN) = 5. So this result is true for any two finite solution sets. 2. If A = {a, c, d, e, f, h, i} and B = {a, b, c, d, g}, solving the solution set for following: n(A), n(B) and n(XnY) Solution: We know that AnB ={a, c, d}. n(A) = 7, n(B) = 5, n(AUB) = 9 and n(AnB) = 3. Therefore the solution set is, n(AUB) = n(A) + n(B) - n(AnB). Practice of solution set online: 1. If A = {1, 3, 4} and B = { 3, 4}, solving A nB. Answer: AnB = {3, 4}. 2. If A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 7}, solving 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}, solving A UB. Answer: AUB = {1, 2, 3, 4, 6}. Learn more on aboutDouble Integral and its Examples. Between, if you have problem on these topics End Behavior, please browse expert math related websites for more help.Please share your comment
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