Question

Using the following information = Universal set = {2,3,4,5,6,7,8,9,12,13,14,16,20,22,56). Subset A = {9,12,13,20,22,56); Subset H= {4,5,8,9,16,22) and Subset C = {1,4,20,22,56} Find: a) P [(AnH)UC] (b) P (HnC)’ (c) P(H)’ (d) P[C\H] (e) P [A\C]

Answer 1

`(2)/(5),(13)/(15),(3)/(5),(1)/(5),(1)/(5)`

Explanation:

The intersection of two sets A and B, denoted by A ∩ B, is the set containing all elements of A that also belong to B.

The union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

`P(s)` of a set
`s` is defined as ratio of number of elements in
`s` to the number of elements in
`universal set`

given
`Universalset=`
`\{`
`\text{2,3,4,5,6,7,8,9,12,13,14,16,20,22,56}`
`\}`

given
`A=\{9,12,13,20,22,56\}` and
`H=\{4,5,8,9,16,22\}`

and
`C=\{1,4,20,22,56\}`

For Question A:

`A`∩
`H`=
`\{9,12,13,20,22,56\}` ∩
`\{4,5,8,9,16,22\}`

=
`\{9,22}\}`

(
`A`∩
`H`)∪
`C`=
`\{9,22}\}` ∪
`C=\{1,4,20,22,56\}`=
`\{1,4,9,20,22,56\}`

`p((A`∩
`H)`∪
`C)`=
`(6)/(15)=(2)/(5)`

For Question B:

`H`∩
`C`=
`\{4,22\}`

`p(H`∩
`C)`'=
`(15-2)/(15)=(13)/(15)`

For Question C:

`p(H)`'=
`(15-6)/(15)=(3)/(5)`

For Question D:

`C`\
`H`=
`\{1,20,56\}`

`p(C`\
`H)`=
`(3)/(15)=(1)/(5)`

For Question E:

`A`\
`C`=
`\{9,12,13\}`

`p(A`\
`C)`=
`(3)/(15)=(1)/(5)`