Operation of Sets 1 Intersection Irisan 2 Union

Operation of Sets 1. Intersection (Irisan) 2. Union (Gabungan) 3. Difference (Selisih) 4. Complement (Komplemen)

Intersection A = {1, 3, 5, 7, 9} B = {2, 3, 5, 7} A B = {3, 5, 7}

Definition � The intersection of sets A and B, written as A B, is a set which consists of all elements common to A and B. � Irisan A dan B ditulis sebagai A B : himpunan yang anngotanya menjadi anggota A sekaligs anggota. � Example : A = set of composite numbers less than 12. B = set of squared numbers less than 20. Determine : a. A B b. n(A B )

Answer If they are stated in the roster method, we get: A = set of composite numbers less than 12. so, A = { 4, 6, 8, 9, 10 } B = set of squared numbers less than 20. so, B = { 1, 4, 9, 16 } a. A B = {4, 9} b. n(A B ) = 2

Union A = {1, 3, 5, 7, 9} B = {2, 3, 5, 7} A B = {1, 2, 3, 5, 7, 9}

Definition �The union of two sets A and B is the set whose elements are elements of A or elements of B, or elements of both sets. �The union of A and B is denoted by A B = { x | x A or x B } �Gabungan himpunan A dan B adalah suatu himpunan yang anggota-anggota nya menjadi anggota A saja atau anggota B saja atau anggota persekutuan A dan B.

Example : A = { 4, 6, 8, 9, 10 } B = { 1, 4, 9, 16 } Determine : a. A B b. n(A B ) Answer : a. A B = {1, 4, 6, 8, 9, 10, 16} b. n (A B ) = 7

The relation n (A B) = n(A) + n(B) – n (A B)

Exercise 1. A = {m, a, d, i, u, n} B = {m, a, n, a, d, o} Determine : a, A B b. A B 2. A = {1, 2, 3, 4, 5, 6} B = {2, 3, 5, 7} Determine : a, A B b. A B

3. P = {x | multiple of 3 less 20} Q = {x | factors of 12} Determine : a. P Q b. P Q 4. Determine a, M b. N c. M N d. M N

5. Determine : a. P b. Q c. P Q d. P Q

DIFFERENCE (selisih) A = {1, 2, 3, 5, 7} B = {2, 3, 5, 7} A = {1, 2, 3, 5, 7} A – B = {1, 9} B – A = {2}

Definition �Given set A and B. Then the difference is: A - B= {x| x A and x B} Himpunan yang anggotanya adalah anggota A tetapi bukan anggota B �B - A= {x| x B and x A} Himpunan yang anggotanya adalah anggota B tetapi bukan anggota A

Example � Given A = { m, a, d, i, u, n} � B = {m, e, d, a, n} � Determine : a. A – B b. B – A b. Answer : a. A – B = { m, a, d, i, u, n} - {m, e, d, a, n} = {i, u} b. B – A = {m, e, d, a, n} - { m, a, d, i, u, n} ={e}

Exercise 1. U = {1, 2, 3, 4, …, 9} A = {1, 2, 3, 4, 5, 6} B = {2, 3, 5, 7} Determine : a. A – B b. B – A 2. P = {the letters that form word “DECEMBER”} Q = {the letters that form word “OCTOBER”} Determine : a. P – Q b. Q – P

3. Determine : a. M – N b. N - M

4. Determine : a. A – B b. B – A

5. Determine : a. P – Q b. Q – P

Complement U = {1, 2, 3, 4, 5, 6} A = {1, 3, 5} A’ = {2, 4, 6}

Complement A’ = {2, 4, 6, 8, 10} B’ = {1, 4, 6, 8, 9, 10}

Definition �Given set A and its universal set is U. �Then the complement of A is : A’ = {x | x U and x A} �Komplemen A : Himpunan yang anggotanya adalah anggota semesta tetapi bukan anggota A

Example U = { 1, 2, 3, . . . , 9 } K = { 3, 4, 5, 6 } Determine : K’ Answer K’ adalah himpunan selain anggota K K’ = {1, 2, 7, 8, 9}

EXERCISE 1. U = {the letters that form word “INDONESIA”} A = {the letters that form word “AFRICA”} Determine : A’ 2. U = {1, 2, 3, 4, …, 9} A = {1, 2, 3, 4, 5, 6} B = {2, 3, 5, 7} Determine : a. A’ b. B’

3. Determine : a. M’ b. N’

4. Determine : a. A’ b. B’

5. Determine : a. P’ b. Q’