Let A = {2, 4, 6, 8}, B = {6, 8, 10, 12} and C = {7, 8, 9, 10}. Find :

(i) A ∪ B

(ii) A ∪ C

(iii) B ∪ C

(iv) A ∩ B

(v) A ∩ C

(vi) B ∩ C

(i) A ∪ B

List all elements from both A and B, avoiding duplicates.

We have:

A = {2, 4, 6, 8}

B = {6, 8, 10, 12}

A ∪ B = {2, 4, 6, 8} ∪ {6, 8, 10, 12}

∴ A ∪ B = {2, 4, 6, 8, 10, 12}

(ii) A ∪ C

List all elements from both A and C, avoiding duplicates.

We have:

A = {2, 4, 6, 8}

C = {7, 8, 9, 10}

A ∪ C = {2, 4, 6, 8} ∪ {7, 8, 9, 10}

∴ A ∪ C = {2, 4, 6, 7, 8, 9, 10}

(iii) B ∪ C

List all elements from both B and C, avoiding duplicates.

We have:

B = {6, 8, 10, 12}

C = {7, 8, 9, 10}

B ∪ C = {6, 8, 10, 12} ∪ {7, 8, 9, 10}

∴ B ∪ C = {6, 7, 8, 9, 10, 12}

(iv) A ∩ B

List all elements common to both A and B.

We have:

A = {2, 4, 6, 8}

B = {6, 8, 10, 12}

A ∩ B = {2, 4, 6, 8} ∩ {6, 8, 10, 12}

∴ A ∩ B = {6, 8}

(v) A ∩ C

List all elements common to both A and C.

We have:

A = {2, 4, 6, 8}

C = {7, 8, 9, 10}

A ∩ C = {2, 4, 6, 8} ∩ {7, 8, 9, 10}

∴ A ∩ C = {8}

(vi) B ∩ C

List all elements common to both B and C.

We have:

B = {6, 8, 10, 12}

C = {7, 8, 9, 10}

B ∩ C = {6, 8, 10, 12} ∩ {7, 8, 9, 10}

∴ B ∩ C = {8, 10}