If A = {6, 7, 8, 9}, B = {4, 6, 8, 10} and C ={x : x ∈ N : 2 < x ≤ 7}; find :

(i) A - B

(ii) B - C

(iii) B - (A - C)

(iv) A - (B ∪ C)

(v) B - (A ∩ C)

(vi) B - B

A = {6, 7, 8, 9}

B = {4, 6, 8, 10}

C ={x :x ∈ N: 2 < x ≤ 7}

C = {3, 4, 5, 6, 7}

(i) A - B

A - B - contains all the elements which are in A but not in B.

A - B = {6, 7, 8, 9} - {4, 6, 8, 10}

A - B = {7, 9}

(ii) B - C

B - C - contains all the elements which are in B but not in C.

B - C = {4, 6, 8, 10} - {3, 4, 5, 6, 7}

B - C = {8, 10}

(iii) B - (A - C)

A - C - contains all the elements which are in A but not in C.

A - C = {6, 7, 8, 9} - {3, 4, 5, 6, 7}

A - C = {8, 9}

B - (A - C) - contains all the elements which are in set B but not in (A - C).

B - (A - C) = {4, 6, 8, 10} - {8, 9}

B - (A - C) = {4, 6, 10}

(iv) A - (B ∪ C)

B ∪ C - contains all the elements in set B and C.

B ∪ C = {4, 6, 8, 10} ∪ {3, 4, 5, 6, 7}

B ∪ C = {3, 4, 5, 6, 7, 8, 10}

A - (B ∪ C) - contains all the elements which is in set A but not in (B ∪ C).

A - (B ∪ C) = {6, 7, 8, 9} - {3, 4, 5, 6, 7, 8, 10}

A - (B ∪ C) = {9}

(v) B - (A ∩ C)

A ∩ C - contains all the common elements in set A and C.

A ∩ C = {6, 7, 8, 9} ∪ {3, 4, 5, 6, 7}

A ∩ C = {6, 7}

B - (A ∩ C) - contains all the elements which is in set B but not in (A ∩ C).

B - (A ∩ C) = {4, 6, 8, 10} - {6, 7}

B - (A ∩ C) = {4, 8, 10}

(vi) B - B

B - B - contains all the elements that are in set B but not in set B.

B - B = {4, 6, 8, 10} - {4, 6, 8, 10}

B - B = ϕ