Identifying universal, equal and equivalent sets,
- 1. IDENTIFYING UNIVERSAL SETS, EQUAL AND EQUIVALENT JOINT AND DISJOINT SETS Ms. G. Martin
- 2. Universal Sets ■ a universal set is a set which contains all objects or all elements under consideration, including itself and denoted by capital U. Example 1. A = {x / x is a vowel in the English alphabet} B = {x / x is a consonant in the English alphabet} Given set A and B, universal set is the set of all letter in the English alphabet. Thus, U = {x / x is a letter in the English alphabet}
- 3. Example 2. Let C = {1, 3, 5, 7, …} D = {2, 4, 6, 8, …} Given the sets C and D, the universal set is the set of counting numbers. Thus, U = {1, 2, 3, 4, 5, 6, 7, …} or U = {x / x is a counting number}
- 4. Equal and Equivalent Sets ■ Two sets are equal if they have the same elements. We write A = B. ■ Two sets are equivalent if they have the same cardinality. That is n(A) = n(B).We write A ↔ B.
- 5. Equal Sets Example 1. A = {x / x is s first 5 multiples of 5} B = {2, 4, 6, 8, 10} A and B are equal sets because they have exactly the same elements. Thus, A = B Example 2. C = { x / x is a whole number less than 9} D = {1, 2, 3, 4, 5, 6, 7, 8} Thus, C = D
- 6. Equivalent Sets Example 1. C = {1, 2, 3, 5, 7} D = {a, e, i, o, u} C and D are equivalent because n(C) = 5 and n(D) = 5. C and D have the same cardinality. Thus, C ↔ D Example 2. E = {apple, mango, banana} F = {x / x is a multiple of 5 less than 17} Thus, E ↔ F
- 7. Joint and Disjoint Sets ■ Sets having common elements are called joint sets. ■ Sets with no common elements are called disjoint sets. Examples: 1. M = {1, 3, 5, 7, 9} and N {2, 4, 6, 8, 10} are disjoint sets 2. P = { 2, 5, 6, 9, 13} and P = {2, 3, 5, 8, 12} are joint sets because they have common elements 2 and 5.