Page 21 - Math 7

Set

Example 4: If U = {1, 2, 3, … 15}, A = {2, 4, 6, 8, 10, 12, 14}, B = {3, 6, 9, 12, 15}, and
C = {2, 3, 5, 7, 11, 13} , list the elements of the following sets.
a) A ‰ B ‰ C b) A ˆ B ˆ C c) (A ‰ B) ˆ C d) (A ˆ B) ‰ C
e) (A ‰ B) – C f) A – (B ˆ C) g) A ‰ B ‰ C h) A ˆ B ˆ C
Solution:
Here, U = {1, 2, 3, …15}, A = {2, 4, 6, 8, 10, 12, 14}, B = {3, 6, 9, 12, 15}
C = {2, 3, 5, 7, 11, 13}
a) A ‰ B = {2, 4, 6, 8, 10, 12, 14} ‰ {3, 6, 9, 12, 15}
= {2, 3, 4, 6, 8, 9, 10, 12, 14, 15}
? A ‰ B ‰ C = (A ‰ B) ‰ C
= {2, 3, 4, 6, 8, 9, 10, 12, 14, 15} ‰ {2, 3, 5, 7, 11, 13}
= {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

b) A ˆ B = {2, 4, 6, 8, 10, 12, 14} ˆ {3, 6, 9, 12, 15}
= {2, 4, 6, 8, 10, 12, 14} ˆ {3, 6, 9, 12, 15} = {6, 12}
? A ˆ B ˆ C = (A ˆ B) ˆ C
= {6, 12} ˆ {2, 3, 5, 7, 11, 13} = I

c) A ‰ B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15}

? (A ‰ B) ˆ C = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15} ˆ {2, 3, 5, 7, 11, 13}
= {2, 3}
d) A ˆ B = {6, 12}
? (A ˆ B) ‰ C = {6, 12} ‰ {2, 3, 5, 7, 11, 13}
= {2, 3, 5, 6, 7, 11, 12, 13}
e) (A ‰ B) = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15}
? (A ‰ B) – C = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15} – {2, 3, 5, 7, 11, 13}
= {4, 6, 8, 9, 10, 12, 14, 15}
f) B ˆ C = {3, 6, 9, 12, 15} ˆ {2, 3, 5, 7, 11, 13} = {3}
? A – (B ˆ C) = {2, 4, 6, 8, 10, 12, 14} – {3}
= {2, 4, 6, 8, 10, 12, 14}

g) A ‰ B ‰ C = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ,15}
? A ‰ B ‰ C = U – (A ‰ B ‰ C)
= {1, 2, 3, …, 15} – {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
= {1}

h) A ˆ B ˆ C = I
? A ˆ B ˆ C = U – {A ˆ B ˆ C} = {1, 2, 3, …15} – I
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 19 Vedanta Excel in Mathematics - Book 7