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Mathematics

If A = {factors of 36} and B = {factors of 48}, find :

(i) A ∪ B

(ii) A ∩ B

(iii) A - B

(iv) B - A

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Answer

A = {factors of 36}

Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

A = {1, 2, 3, 4, 6, 9, 12, 18, 36}

B = {factors of 48}

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

B = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

(i) A ∪ B

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

A ∪ B = {1, 2, 3, 4, 6, 9, 12, 18, 36} ∪ {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

A ∪ B = {1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48}

(ii) A ∩ B

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

A ∩ B = {1, 2, 3, 4, 6, 9, 12, 18, 36} ∩ {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

A ∩ B = {1, 2, 3, 4, 6, 12}

(iii) A - B

A - B - contains all the elements in set A but not in B.

A - B = {1, 2, 3, 4, 6, 9, 12, 18, 36} - {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

A - B = {9, 18, 36}

(iv) B - A

B - A - contains all the elements in set B but not in A.

B - A = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48} - {1, 2, 3, 4, 6, 9, 12, 18, 36}

B - A = {8, 16, 24, 48}

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