Question

Let A, B and C be the sets: . A={1,3,5,6,8,10} • B = {2,3,6,9} • C = {1,5,7) Write these as sets explicitly (list all possible elements enclosed within {}). (a) AUB (b) Bnc (c) A-B (d) BxC (C) PIC).

Answer 1

(a)
`A\cup B=\{1,2,3,5,6,8,9,10\}`

(b)
`B\cap C=\{\}`

(c)
`A-B=\{1,5,8,10\}`

(d)
`B* C=\{(2,1),(2,5),(2,7),(3,1),(3,5),(3,7),(6,1),(6,5),(6,7),(9,1),(9,5),(9,7)\}`

(e)
`P(C)=\{\{\},\{1\},\{5\},\{7\},\{1,5\},\{1,7\},\{5,7\},\{1,5,7\}\}`

Explanation:

Given information:

A, B and C are three sets:

A={1,3,5,6,8,10}, B = {2,3,6,9}, C = {1,5,7}

A set contains distinct elements.

(a)

We need to find the set AUB. In this set all elements of A and B are included.

`A\cup B=\{1,2,3,5,6,8,9,10\}`

(b)

We need to find the set B∩C. In this set all common elements of B and C are included.

`B\cap C=\{\}`

It is an empty set because there is no common element in set B and C.

(c)

We need to find the set A-B. In this set all elements of A are included excluding the common elements of A and B.

`A-B=\{1,5,8,10\}`

(d)

We need to find the set BxC.

BxC is defined as

`B* C=\{(x,y):x\in B,y\in C\}`

`B* C=\{(2,1),(2,5),(2,7),(3,1),(3,5),(3,7),(6,1),(6,5),(6,7),(9,1),(9,5),(9,7)\}`

(e)

We need to find the set P(C). It is a power set of C. It is the collection of all subsets of set C.

`P(C)=\{\{\},\{1\},\{5\},\{7\},\{1,5\},\{1,7\},\{5,7\},\{1,5,7\}\}`