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Sets and Subsets

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Sets and Subsets

1. 1. (Sets and Subsets)
2. 2. A different look at circles <ul><li>Set A Set B </li></ul><ul><li> Set C </li></ul>
3. 3. <ul><li>In an excursion at Pagsanjan Falls, 80 students brought sandwiches, drinks and canned goods as follows: </li></ul><ul><li>50 students brought sandwiches </li></ul><ul><li>30 students brought drinks </li></ul><ul><li>30 students brought canned goods </li></ul><ul><li>18 students brought canned goods and drinks </li></ul><ul><li>15 students brought sandwiches and canned goods </li></ul><ul><li>8 students brought sandwiches and drinks </li></ul><ul><li>5 students brought sandwiches, canned goods and drinks </li></ul><ul><li>Question: </li></ul><ul><li>How many students did NOT bring any of the 3 kinds? </li></ul>
4. 4. <ul><li>SET </li></ul><ul><li>- a well defined collection of distinct objects </li></ul><ul><li>- CAPITAL LETTERS are used to represents set </li></ul><ul><li>Example: </li></ul><ul><li>A = {1, 2, 3, 4, 5} </li></ul><ul><li>B = { M, A, T, H} </li></ul><ul><li>C = { all even numbers} </li></ul>
5. 5. <ul><li>ELEMENT </li></ul><ul><li>- pertains to each object in a set </li></ul><ul><li>- denoted by the symbol ______ which is read as &quot;element of set ____” while the symbol____means “NOT an element of set _____” </li></ul><ul><li>Example: </li></ul><ul><li>A ={ 1, 2, 3, 4, 5} </li></ul><ul><li>3 ____ of set A </li></ul><ul><li>7 _____ of set A </li></ul>
6. 6. <ul><li>BRACES { } </li></ul><ul><li>- are used to enclose the elements of a given set </li></ul><ul><li>Example: </li></ul><ul><li>A = { x | x is an even </li></ul><ul><li>integer} </li></ul><ul><li>Set is read as “the set of all elements x, such that x is an even integer” </li></ul><ul><li>B = { x | x is a letter in the </li></ul><ul><li>word Math} </li></ul><ul><li>“ the set of all elements of x, such that x is a letter in the word Math” </li></ul>
7. 7. <ul><li>A = {x | x is a multiple of 3 between 3 and 18 } </li></ul><ul><li>B = { x | x is a letter in the word Algebra} </li></ul><ul><li>C ={ x | x is a positive odd number } </li></ul><ul><li>A = { 3, 6, 9, 12, 15 } </li></ul><ul><li>B = {A, L, G, E, B, R } </li></ul><ul><li>C = {1,3, 5, 7, 9, 11, 13, ….} </li></ul>ROSTER/LISTING METHOD
8. 8. Kinds of Sets: <ul><li>FINITE SET </li></ul><ul><li>- a set whose number of elements can be counted </li></ul><ul><li>Example: </li></ul><ul><li>A = { -1, -2, -3, -4, -5 } </li></ul><ul><li>B = { x | x is a multiple of 5 between 10 and 50} </li></ul><ul><li>C = { x | x is a letter in the Philippine alphabet } </li></ul>
9. 9. Kinds of Sets: <ul><li>INFINITE SET </li></ul><ul><li>- a set whose number of elements CAN NOT be counted </li></ul><ul><li>Example: </li></ul><ul><li>A = { -1, -2, -3, -4, -5, . . . } </li></ul><ul><li>B = { x | x is a </li></ul><ul><li>multiple of 5 } </li></ul><ul><li>C = { x | x is a name </li></ul><ul><li>of a person} </li></ul>
10. 10. Kinds of Sets: <ul><li>NULL / EMPTY SET </li></ul><ul><li>- a set that has NO element </li></ul><ul><li>- denoted by { } or O </li></ul><ul><li>Example: </li></ul><ul><li>A = { } </li></ul><ul><li>B = O </li></ul>
11. 11. <ul><li>EQUIVALENT SETS </li></ul><ul><li>- two or more sets that have the same number of elements </li></ul><ul><li>Example: </li></ul><ul><li>A = {2, 4, 6, 8, 10 } </li></ul><ul><li>B = { a, b, c, d, e} </li></ul><ul><li>Sets A and B are </li></ul><ul><li>equivalent sets. </li></ul>
12. 12. <ul><li>EQUAL SETS </li></ul><ul><li>- two or more </li></ul><ul><li>sets that have the </li></ul><ul><li>same elements </li></ul><ul><li>Example: </li></ul><ul><li>A = {2, 4, 6, 8, 10 } </li></ul><ul><li>B = { 2, 4, 6, 8, 10 } </li></ul><ul><li>Sets A and B are </li></ul><ul><li>equal sets. </li></ul>
13. 13. <ul><li>UNIVERSAL SET </li></ul><ul><li>- the TOTALITY of ALL the elements in two or more given sets </li></ul><ul><li>- denoted by “ U ” </li></ul><ul><li>Example: </li></ul><ul><li>A = { 2, 4, 6, 8 } </li></ul><ul><li>B = { 1, 2, 3, 4 } </li></ul><ul><li>U = { 1, 2, 3, 4, 6, 8} </li></ul><ul><li>A = { a, b, c, d, e } </li></ul><ul><li>B = { a, e, i, o, u } </li></ul><ul><li>U = { a, b, c, d, e, i, o, u} </li></ul>
14. 14. <ul><li>SUBSET </li></ul><ul><li>- Set B is a subset of Set A if and only if ALL the elements in set B is in Set A </li></ul><ul><li>Example: </li></ul><ul><li>A = { 2, 4, 6, 8 } </li></ul><ul><li>B = { 2, 4, 8 } </li></ul><ul><li>Set B is a subset of Set A </li></ul><ul><li>A = { a, b, c, d, e } </li></ul><ul><li>B = { a, e, i, o, u } </li></ul><ul><li>Set B is NOT a subset of Set A </li></ul>