Math
In math class this quarter we studied about sets and Venn diagrams. There are a lot of symbols used for this topic such as intersection, union, element, and more. So before we studied about sets and Venn diagrams we researched it first so we could know each meaning of the symbols, the ways to do it, and more. The research it self contains the meaning of each, an example of problem, and more.
Set and Venn Diagram
Geral, Josephine, Tibo
Math Standard Level
4 May 2012
Set and Venn Diagram
Math in general is a term we might hear every single day, and every single minute of our lives. Even days and minutes itself is a mathematical term. We might not realize it but in everything we do, math will be used. On this essay, the specific topic/term that will be discussed is about Set and Venn Diagram.
Set and Venn Diagram are two different word/phrase in the English Language. According to its dictionary definition, venn diagram is defined as "A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles." and set is defined as " A group or collection of things that belong together, resemble one another, or are usually found together". Even so, in math Set and Venn Diagram is clarified to be a theory that calculates a "collection" of objects on numbers in a Venn Diagram.
The key term 'set' means "a collection of things, without regard to their order". In the mathematical view of Set and Venn Diagram, the theory can be used to calculate a collection of things and/or numbers. Sets could be a number of things, a group of numbers, letters or even words. Set notation always use French brasses to start {number/things}. Each sets desire have a meaning, the number/things shouldn’t be repeated in a set and the list of numbers or things could be in no particular order. By using a Venn diagram it could represent sets visually. Venn diagrams has two circles with three parts, O()O. To represent sets with Venn diagram it should at least have two sets (set A and B). The left side of the circle is one of the set (set A), the right side of the circle would be a set also (set B). So two circles represent two sets, and these two circles are called the Union. Union is the number or object from sets of A or B or both in a two circle. In the middle would be the similar things or numbers in both sides of the circles. The middle circle is called the intersection. Intersection is those numbers or things which are in Set A or B. Actually a Venn diagram is according to the number of sets, if there are three sets than there would be three circles with approximately seven parts. But most common Venn diagram is two circles with three parts comparing only two sets. So Venn diagram helps sets to be more understandable by showing it visually, it helps us to compare two or more different sets easily.
Example of two sets (set A and B and Venn Diagram):
A real-life problems that needed/uses Set and Venn Diagram as a calculating device for example is when grouping things. Here is an example to show how Set and Venn Diagram works
Example:
Question: There are twenty-four dogs are in a kennel. Twelve of the dogs are black, six of the dogs have short tails, and fifteen of the dogs have long hair. There is only one dog that is black with a short tail and long hair. Two of the dogs are black with short tails and do not have long hair. Two of the dogs have short tails and long hair but are not black. If all of the dogs in the kennel have at least one of the mentioned characteristics, how many dogs are black with long hair but do not have short tails?
Solution: (Picture)
9 - x + 2 + 1 + 1 + 2 + x + 12 - x = 24
27 - x = 24
x = 3
As to how it is also used in making decisions and choices in our daily lives, it also has some advantage and disadvantages that is needed to be carefully understood. On of the disadvantage that can be point out is that it is a complicated method for those who need speed on solving some problems on certain occasions. The advantage that can also be pointed out is the fact that it is very universal on to what is can be used for. Some examples that is provided is the need of grouping different things such as people, plants, animals and many other things that can continue on with this list.
As a conclusion the theory of Set and Venn Diagram can be useful for real-life problems that includes decision making, and groupings of things and/or number. It may have some advantages and disadvantage that is needed to be understood. Everything in life has advantages and disadvantages, not excluding Set and Venn diagram, which is why this method/theory of grouping/decision making is a useful method for beginners.
Bibliography:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i1/bk7_1i3.htm
http://www.math.hawaii.edu/~williamdemeo/Math371-Summer2011/SetOperationsAndVenDiagrams.pdf
http://www.mathsisfun.com/sets/venn-diagrams.html
http://www.regentsprep.org/Regents/math/ALGEBRA/AP2/LVenn.htm
http://www.purplemath.com/modules/venndiag2.htm
http://www.shodor.org/interactivate/lessons/SetsTheVennDiagram/
http://childparenting.about.com/od/schoollearning/a/venn_diagram_def.htm
http://searchsecurity.techtarget.com/definition/set
http://math.wikia.com/wiki/Set
Math Standard Level
4 May 2012
Set and Venn Diagram
Math in general is a term we might hear every single day, and every single minute of our lives. Even days and minutes itself is a mathematical term. We might not realize it but in everything we do, math will be used. On this essay, the specific topic/term that will be discussed is about Set and Venn Diagram.
Set and Venn Diagram are two different word/phrase in the English Language. According to its dictionary definition, venn diagram is defined as "A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles." and set is defined as " A group or collection of things that belong together, resemble one another, or are usually found together". Even so, in math Set and Venn Diagram is clarified to be a theory that calculates a "collection" of objects on numbers in a Venn Diagram.
The key term 'set' means "a collection of things, without regard to their order". In the mathematical view of Set and Venn Diagram, the theory can be used to calculate a collection of things and/or numbers. Sets could be a number of things, a group of numbers, letters or even words. Set notation always use French brasses to start {number/things}. Each sets desire have a meaning, the number/things shouldn’t be repeated in a set and the list of numbers or things could be in no particular order. By using a Venn diagram it could represent sets visually. Venn diagrams has two circles with three parts, O()O. To represent sets with Venn diagram it should at least have two sets (set A and B). The left side of the circle is one of the set (set A), the right side of the circle would be a set also (set B). So two circles represent two sets, and these two circles are called the Union. Union is the number or object from sets of A or B or both in a two circle. In the middle would be the similar things or numbers in both sides of the circles. The middle circle is called the intersection. Intersection is those numbers or things which are in Set A or B. Actually a Venn diagram is according to the number of sets, if there are three sets than there would be three circles with approximately seven parts. But most common Venn diagram is two circles with three parts comparing only two sets. So Venn diagram helps sets to be more understandable by showing it visually, it helps us to compare two or more different sets easily.
Example of two sets (set A and B and Venn Diagram):
A real-life problems that needed/uses Set and Venn Diagram as a calculating device for example is when grouping things. Here is an example to show how Set and Venn Diagram works
Example:
Question: There are twenty-four dogs are in a kennel. Twelve of the dogs are black, six of the dogs have short tails, and fifteen of the dogs have long hair. There is only one dog that is black with a short tail and long hair. Two of the dogs are black with short tails and do not have long hair. Two of the dogs have short tails and long hair but are not black. If all of the dogs in the kennel have at least one of the mentioned characteristics, how many dogs are black with long hair but do not have short tails?
Solution: (Picture)
9 - x + 2 + 1 + 1 + 2 + x + 12 - x = 24
27 - x = 24
x = 3
As to how it is also used in making decisions and choices in our daily lives, it also has some advantage and disadvantages that is needed to be carefully understood. On of the disadvantage that can be point out is that it is a complicated method for those who need speed on solving some problems on certain occasions. The advantage that can also be pointed out is the fact that it is very universal on to what is can be used for. Some examples that is provided is the need of grouping different things such as people, plants, animals and many other things that can continue on with this list.
As a conclusion the theory of Set and Venn Diagram can be useful for real-life problems that includes decision making, and groupings of things and/or number. It may have some advantages and disadvantage that is needed to be understood. Everything in life has advantages and disadvantages, not excluding Set and Venn diagram, which is why this method/theory of grouping/decision making is a useful method for beginners.
Bibliography:
http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i1/bk7_1i3.htm
http://www.math.hawaii.edu/~williamdemeo/Math371-Summer2011/SetOperationsAndVenDiagrams.pdf
http://www.mathsisfun.com/sets/venn-diagrams.html
http://www.regentsprep.org/Regents/math/ALGEBRA/AP2/LVenn.htm
http://www.purplemath.com/modules/venndiag2.htm
http://www.shodor.org/interactivate/lessons/SetsTheVennDiagram/
http://childparenting.about.com/od/schoollearning/a/venn_diagram_def.htm
http://searchsecurity.techtarget.com/definition/set
http://math.wikia.com/wiki/Set
Reflection
In this subject there are a lot of test. I put much effort during the test, I always studied before the test. But there are some questions that are really hard (unfamiliar question) which I can't answered that caused me not to get a perfect score. But my score are still pretty good at least I put didn't gave up when doing the test. I should also start to often double check my work, because in the test there is a question that where I was wrong calculation (small mistakes).
The IB learner profile would be Reflective, because I always reflect back on what I did wrong and didn't do it again in the next test. From the reflected mistakes I have done I hope it won't happened again.
The IB learner profile would be Reflective, because I always reflect back on what I did wrong and didn't do it again in the next test. From the reflected mistakes I have done I hope it won't happened again.