Q6 of 71 Page 23

i. If U = {x : 0 ≤ x ≤ 10, } and A = {x : x is a multiple of 3}, find A’

ii. If U is the set of natural numbers and A’ is the set of all composite numbers, then what is A?

i. U = {x : 0 ≤ x ≤ 10, x ∈}


U contains all the whole numbers that are greater than or equal to zero and less than or equal to 10.


∴ U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}


A = {x : x is a multiple of 3}


Multiples of 3 present in U are : 3, 6, 9 [U→ Universal set]


∴ A = {3, 6, 9}


∴ A’ = {0, 1, 2, 4, 5, 7, 8, 10} [element that are present in U but not in A]


ii. U is the set of natural numbers.


A’ is the set of all composite numbers.


⇒ (A’)’ = A


∴ A contains all the elements that are present in U but not in A’.


∴ A contains all the natural numbers that are not composite numbers.


∴ A is the set of all prime numbers and 1.


More from this chapter

All 71 →
4

U = {1, 2, 3, 6, 7, 12, 17, 21, 35, 52, 56},

P = {numbers divisible by 7}, Q = {prime numbers}


List the elements of the set {x : x ∈ P ∩ Q}

 5

State which of the following sets are disjoint

i. A = {2, 4, 6, 8}; B = {x : x is an even number < 10, }


ii. X = {1, 3, 5, 7, 9}, Y = {0, 2, 4, 6, 8, 10}


iii. P = {x : x is a prime < 15}


Q = {x : x is a multiple of 2 and x < 16}


iv. R = {a, b, c, d, e}, S = {d, e, a, b, c}

 7

If U = {a, b, c, d, e, f, g, h}, A = {a, b, c, d} and B = {b, d, f, g},

Find


i. A ∪ B


ii. (A ∪ B)’


iii. A ∩ B


iv. (A ∩ B)’

 8

If U = , A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 9, 10},

Find


i. A’


ii. B’


iii. A’ ∪ B’


iv. A’ ∩ B’