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Note that some sections will have more problems than others and some will have more or less of a variety of problems. Here are a set of practice problems for the Algebra notes. How is Set Theory important? (a) The collection of all alphanumeric characters. The second way of defining a set is as shown above with the pictures of the cars. This symbol is often called the empty set. Children who can visualize mathematical concepts will take to set theory far easily than children who have difficulty visualizing. For equations that will mean that the right side of the equation will not equal the left side of the equation. In this case we will say that a number will satisfy the inequality if, after plugging it in, we get a true inequality as a result. OTHER TOPICS Profit and loss shortcuts. However, due to the immense stress laid on definitions over concepts, it appears to be a lot harder than it actually is. Since we have two toys that are common to both these collections, they are only counted once in the Union. The first way is done by describing it in words. So, we want to see if \(y = 8\) satisfies the equation. It is known as the, In simple words, the union of two sets X and Y have distinct objects that are present in set X, In simple words, the intersection of two sets X and Y have objects that are present in set X, Visualising Union and Intersection - Venn Diagrams, Another visually beautiful way of representing the union and intersection of two or more sets is by using. This is the same inequality with a different value so let’s check that. 1 Is each of the following a well-defined set? The first way is done by describing it in words. While this can be confusing at times, it’s actually quite easy. 32 and 36 from section 2.4 . Set Theory happens to be one of the easiest mathematical concepts taught in school. Remember to solve doubts if a child is struggling with a concept. There is also some formal notation for solution sets although we won’t be using it all that often in this course. Set Theory Exercise 1 . Wellesley-Cambridge Press, 2009. Sometimes children do not fully understand the concept of distinct objects. Search . Venn Diagrams make Set Theory a lot easier to understand. A popular yet effective way of teaching set theory is by assigning physical objects to the children in the classroom. A set is a collection of distinct objects, so suppose we defined a set of cars, it would look something like this: Set A = {, ,  ,          ,          ,          }. Now, there is no reason to think that a given equation or inequality will only have a single solution. Word problems on constant speed. For example, A is a set whose members are cars. In this case, both X and Y have the dark blue car and Hungry Hippos in common, so they are the only objects in the intersection. Depending on the complexity of the inequality the solution set may be a single number or it may be a range of numbers. That means C is a set whose members are the colours red, green and blue. (d) The collection of all integers x for which: 2x – 9 = 16. (e) The collection of all good tennis players. However, for the vast majority of the equations and inequalities that we will be looking at will have simple enough solution sets that it’s just easier to write down the solutions and let it go at that. Squaring \(x\) makes \(x\) greater than equal to zero, then adding 1 onto that means that the left side is guaranteed to be at least 1. Suppose there was a toy box of toys, and X enjoyed playing with a few toys, and Y enjoyed playing with a few toys. It is known as the extensional definition, which is just a fancy way of enclosing the members of a set within curly brackets. B is a set of six positive integers. ASSn # ASSIGNMENTS SOLUTIONS; Problem set 1: Do problems: 23 and 28 from section 1.2.