powerpoint presentation

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.