Let U x Z 5 x 10 Suppose A 1 0 1 2 3 B 0 2 4 6 8 10 and

Let U = {x Z | 5 x 10}. Suppose A = {1, 0, 1, 2, 3}, B = {0, 2, 4, 6, 8, 10}, and C = {1, 0, 6, 7, 8, 9, 10}

a) List the elements of A C

b) List the elements of A B

c) List the elements of A (B C)

Solution

A) The UNION of two sets is the set of elements which are in either set.

A = {1, 0, 1, 2, 3} and C = {1, 0, 6, 7, 8, 9, 10}. Now the UNION of A and C, written AC = {1, 0, 1, 2, 3, 6, 7, 8, 9, 10 }. There is no need to list the -1 & 0 twice.

B)The INTERSECTION of two sets is the set of elements which are in both sets.

A = {1, 0, 1, 2, 3} and B = {0, 2, 4, 6, 8, 10}. The INTERSECTION of A and B, written A   B = {0, 2}.

C) Firstly we have to find out the union of B & C Sets

B = {0, 2, 4, 6, 8, 10},

C = {1, 0, 6, 7, 8, 9, 10}

B C= {0, 2, 4, 6, 8, 10} U {1, 0, 6, 7, 8, 9, 10}

B C ={-1,0, 2, 4, 6, 7, 8, 9, 10},

A (B C) = Difference: i.e, elements in A but not in B C

Therefore A (B C) =(1, 0, 1, 2, 3) - {-1,0, 2, 4, 6, 7, 8, 9, 10}

A (B C) ={1,3}