Question

If U=( 1,2,3,4,5,6,7,8,9,10) A=(1,2,4,5) B=(2,4,6,8) C=(2,3,5,7,9) find i) AuB ii) AnBnC iii) BnC iv)A' v)B' vi) A'nB' vii) A'uC'

Answer 1

i) AuB is the union of sets A and B. To find this, we combine all the elements from both sets, removing any duplicates:
U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
A = (1, 2, 4, 5)
B = (2, 4, 6, 8)

Combining A and B, we get:
AuB = (1, 2, 4, 5, 6, 8)

ii) AnBnC is the intersection of sets A, B, and C. To find this, we identify the elements that are common to all three sets:
C = (2, 3, 5, 7, 9)

AnBnC = (2)

iii) BnC is the intersection of sets B and C. To find this, we identify the elements that are common to both sets:
BnC = (2)

iv) A' is the complement of set A, which means it includes all the elements in U that are not in A. To find this, we subtract the elements of A from U:
A' = (3, 6, 7, 8, 9, 10)

v) B' is the complement of set B, which means it includes all the elements in U that are not in B. To find this, we subtract the elements of B from U:
B' = (1, 3, 5, 7, 9, 10)

vi) A'nB' is the intersection of the complement of A and the complement of B. To find this, we identify the elements that are common to both sets:
A'nB' = (3, 7, 9, 10)

vii) A'uC' is the union of the complement of A and the complement of C. To find this, we combine all the elements from both sets, removing any duplicates:
A' = (3, 6, 7, 8, 9, 10)
C' = (1, 4, 6, 8, 10)

Combining A' and C', we get:
A'uC' = (1, 3, 4, 6, 7, 8, 9, 10)