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  • 1. Name: Allen Veejay P. Corpuz<br />Age: 16<br />Birthday: September, 24 1993<br />Address in Lucban: Miramonte Lucban,Quezon<br />Address in Hometown: Famy,Laguna<br />Cell phone no: 09306970901<br />Telephone no: 0495011559<br />Hobbies: Surfing in Internet<br />Mother`s name: Emilita Corpuz<br />Father`s name: Alberto Corpuz<br />Lesson 1<br />Lecture no.1<br /> Group- a basic structure of modern algebra, consisting of a set of elements and an operation. The operation takes any two elements of the set and forms another element of the set in such a way that certain conditions are met. The theory of groups is the subject of intense study within mathematics, and is used in many scientific fields. For example, groups are used in chemistry to describe the symmetries of molecules, and the Lorentz group is a central part of special relativity. Also, the theory of groups plays a central role in particle physics, where it has led to the discovery of new elementary particles.<br />An example of a group is the set of all numbers, including the negative numbers and zero, with the usual operation of addition. The operation + (sum) takes two numbers such as 3 and 7 and forms their sum: 3 + 7. Addition of numbers also has the three properties listed below; these properties are common to all groups. In a general group, the operation ∘ takes two elements such as x and y and forms the element x∘y.<br />Sets- collection of objects of any sort, such as numbers, geometric figures, or functions. The notation {5, 7, 8}, for example, indicates a set consisting of the numbers 5, 7, and 8. A set containing no elements at all, {}, is called an empty set. See also Set Theory.<br />Null set-also called null set, set that has no elements or members. The set of members common to the sets {2,3,4} and {7,8,9}, for example, is empty: There are no members that belong to both sets. The symbols Æ and {} are often used to stand for the empty set<br />Methtod<br />*roster <br /> N={1,2,3. . . }<br /> N={x/x EN}<br />*set-builder notation<br /> J={x/x is negative nos.}<br /> J= {-3,-2,-1} <br />*rule<br /> 1EN null set<br /> -1EN Q=x/x EN, X=0<br /> -1EJ Q={}or Q=0 <br /> <br />C={1,2,3,4} Z=integer<br />C={x/EN,1<x<4} N=natural nos. <br />C=x/xEN,x<5} R=real nos.<br /> Q=rational nos.<br /> W=whole nos.<br />*some elements and some cardinal=are equal <br />A={1,2,3,4} A={1,2,3,4} n(A)=4 A~B <br />B={x/x EW} B={a,b,c,d} n(B)=4 B~C <br /> C={1,6/3,9/3,12/3} n(C)=4 A~C<br />Comment:<br /> It’s so hard to understand because it’s our first lecture so I’m adjusting myself to it, and so difficult to understand so I must let myself to study on my own.<br />Lecture no. 2<br />Relation of Sets- Equality or equivalence.<br />Subset-a set, or collection of real or hypothetical objects, all of whose elements are contained in another set. <br /> N=4 <br />Subsets {} 1<br /> {1}{2}{3]{4} 4<br /> {1,2}{1,3}{1,4}{2,3}{2,4}{3,4} 6<br /> {1,2,3}{1,2,4}{2,3,4}{1,3,4} 4<br /> {1,2,3,4} 1<br />A={1,2,3,4}<br />B={1} BCA<br />C={1,2,3} CCB<br />Power set P(A)=2 with the power of n<br /> =2 with the power of 4<br /> = n=4 therefore the answer is 16<br />Pascal Triangle<br /> 1<br /> 1 1<br /> 1 2 1<br /> 1 3 3 1<br /> 1 4 6 4 1<br /> 1 5 10 10 5 1<br /> 1 6 15 20 15 6 1<br /> 1 7 21 35 35 21 7 1<br />Comment:<br /> I don’t even an idea that we are talking about because, we did not tackle when we are high school lesson we tackle it but is our teacher not explaned it so well.<br />Lecture no.3<br />Operation-In its simplest meaning in mathematics and logic, an operation is an action or procedure which produces a new value from one or more input values. There are two common types of operations: unary and binary. Unary operations involve only one value, such as negation and trigonometric functions. Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, and exponentiation.<br />Union- set consisting of all elements that are members of two or more given sets joined together. The union of the sets {1, 2, 3} and {4, 5}, for example, is {1, 2, 3, 4, 5}. The È symbol is often used to indicate the union of two sets: {1, 2, 3} È {4, 5}. <br /> <br />1.Union of AUB ={x/xEA or xEB} <br /> A={a,b,c,d}<br /> B={b,e,f,g}<br /> AUB={a,b,de,f,g}<br /> Intersection of A and B={b,e}<br />Intersection-the intersection (denoted as ∩) of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.<br />2.Intersecton AUB= {x/xEA and xEb}<br /> <br />Complement-complement, an operation that transforms an integer into its additive inverse, useful for subtracting numbers when only addition is possible, or is easier<br />A’={4,5,6,7} A’={3,7,8,9}<br /> B’={5,6,8,9}<br />A+B =B+A<br />A-B= is not equal to B-A<br />A-B[x/EA,xEB}<br />B-A{x/xEB,xEA}<br />Comment:<br /> I`am so so confuse because by means how to use the three different procedure,and I’am confuse too how to use it.<br />Lesson 2<br />Lecture no.4<br />Closure- a set is said to be closed under some operation if performance of that operation on members of the set always produces a member of the set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 7 are both natural numbers, but the result of 3 − 7 is not.<br />Let a,b,c,d E R<br />a+b E R<br />a.b E R<br /> <br />Commutative order<br /> a+b=b+a<br /> a.b=b.a<br />Association grouping<br /> a+(b+c)=ab+ac<br />Distributive<br /> a(a+c)=ab+ac<br />Identity<br /> a+0=a<br />Zero property<br /> a.0=0<br /> a=1<br /> 100=1<br />Algebraic Expression<br />Variable-a letter that represents a value in an algebraic expression.<br />Constant-is a special number, usually a real number, that arises naturally in mathematics. Unlike physical constants, mathematical constants are defined independently of physical measurement.<br />Operation-In its simplest meaning in mathematics and logic, an operation is an action or procedure which produces a new value from one or more input values. There are two common types of operations: unary and binary. Unary operations involve only one value, such as negation and trigonometric functions. Binary operations, on the other hand, take two values, and include addition, subtraction, multiplication, division, involution, and evolution.<br />Coefficient-The Coefficient of a term in an expression is the number which is multiplied by one or more variables or powers of variables in the term.<br />5x y =5.x.x.y.y.y.y<br /> 5x =x y<br /> y =5 x y<br /> y =5 x y<br />Monomial- one term<br />Binomial- two term<br />Trinomial- three term<br />Multinomial- two or more term<br />Comment:<br /> I understand it so well because I have my focus to listen to our teacher although we tackle it already our C.I elaborate it so clear.<br />