* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download INEQUALITIES
Survey
Document related concepts
History of mathematical notation wikipedia , lookup
Positional notation wikipedia , lookup
Ethnomathematics wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Large numbers wikipedia , lookup
Non-standard analysis wikipedia , lookup
Surreal number wikipedia , lookup
Real number wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Birkhoff's representation theorem wikipedia , lookup
Elementary mathematics wikipedia , lookup
Transcript
Madania Secondary School Grade 7 Mathematics Worksheet Name: ________________________________ Class: 7_ Date: __________ Terms in Sets and Venn Diagram WHAT’S A SET? A set is a well-defined collection of any kind of objects: people, ideas, plants, numbers, responses, etc. e.g. 1. M is a set of Math teachers at SMP Madania. 2. P is a set of prime numbers less than 10. 1112-S1-G7-MA-WS-W18-TYS-LBR-111129-Terms in Sets and Venn diagram 1 NOTATION FOR SETS A. LISTING THE ELEMENTS 1. M is the set Math teachers at SMP Madania. M = {_____, _____, _____, _____} 2. P is the set of whole numbers less than 4. P = {__, __, __, __} B. WRITING THE PROPERTY CHARACTERIZING THE ELEMENTS 1. M is the set Math teachers at SMP Madania. __ = {x|x _______________________________________} 2. P is the set of whole numbers less than 4. __ = {x|x ________________________________} 2 WHAT’S A VENN DIAGRAM? A Venn diagram is a diagram where sets are represented as simple geometric figures, with overlapping and similarity of sets represented by intersections and unions of the figures. What does this Venn diagram represent? ___ ●__ ●__ ●__ B A ●__ ●__ ●__ ●__ ●__ ●__ A = The set of multiples of 3 between 0 and 10. → A = {__, __, __} B = The set of even numbers between 0 and 10. → B = {__, __, __, __} 3 What do the symbols mean? The set of all individuals in which you are interested is called the universe . UNIVERSE U = {__, __, __, __, __, __, __, __, __} ___ ●__ ●__ ●__ B A ●__ ●__ ●__ ●__ ●__ ●__ A = The set of multiples of 3 between 0 and 10. → A = {__, __, __} B = The set of even numbers between 0 and 10. → B = {__, __, __, __} 4 What do the symbols mean? ELEMENT The objects belonging to a set are called its members or elements. & NOT ELEMENT __ __ __ __ __ B A ●__ ●__ ●__ ●__ ●__ ●__ __ __ __ __ A = The set of multiples of 3 from 2 until 7. → A = {__, __} B = The set of even numbers from 2 until 7. → B = {__, __, __} 5 What do the symbols mean? COMPLEMENT ~A = {__, __, __, __, __} The complement of a set A is the set of all those elements of the universal set which are not in A. ~B = {__, __, __, __, __} __ B A B A ●__ ●__ ●__ ●__ ●__ ●__ __ ●__ ●__ ●__ A is the set of odd numbers between 2 and 8. ●__ ●__ ●__ ●__ ●__ ●__ ●__ B is the set of odd numbers from 5 until 10. 6 What do the symbols mean? DIFFERENCE A - B = {__, __} __ B - A = {__} __ B A ●__ ●__ The difference of A and B means the elements which belong A to but not to B. ●__ ●__ A is the set of whole numbers less than 3. B A ●__ ●__ ●__ ●__ B is the set of natural numbers between 1 & 4. 7 What do the symbols mean? INTERSECTION AB The intersection of two sets A and B is the set whose elements are common to both A and B. = {__} __ B A ●__ ●__ ●__ ●__ A is the set of prime numbers less than 7. B is the set of prime numbers less than 10 but greater than 4. 8 What do the symbols mean? The union of two sets A and B is the set which contains all the elements of A and all the elements of B (and hence all the elements which are in both A and B). UNION AB = {____________} __ A B A is the set of whole numbers less than 6. B is the set of prime numbers less than 10 but greater than 4. 9 What do the symbols mean? SUBSET Set A is called a subset of set B if all the elements of A are inside set B. AB __ B A A = The set of multiples of 4 between 0 and 10. B = The set of even numbers between 0 and 10. 10 What do the symbols mean? DISJOINT SETS & NULL/EMPTY SET Ø C // D C If C and D have no common elements, that is, their intersection is the null set/empty set: C D = Ø, then they are said to be disjoint sets. C = _________________________ __ D ______________________. D = _________________________ ______________________. 11 What do the symbols mean? EQUAL SETS Two sets E and F are said to be equal if they contain exactly the same members. E=F E = _________________________ __ F E ______________________. F = _________________________ ______________________. 12 What do the symbols mean? EQUIVALENT SETS X is equivalent with Y if the number of elements in set X is the same as the number of elements in Y. X~Y X __ Y X = _________________________ ______________________. Y = _________________________ ______________________. 13 EQUIVALENT SETS vs EQUAL SETS If X ___ Y, then for sure X ___ Y. If X ___ Y then it is possible that X ___ Y PRESENTING THE NUMBER OF ELEMENTS IN A SET e.g. A = {cat, dog, bird, fish, iguana, rabbit} There are __ elements in set A, then it written as: __(__) = ___ 14