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Mathematics

If P = {factors of 36} and Q = {factors of 48} ; find :

(i) P ∪ Q

(ii) P ∩ Q

(iii) Q - P

(iv) P' ∩ Q

Sets

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Answer

P = {factors of 36}

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

Q = {factors of 48}

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

(i) P ∪ Q

P ∪ Q - contains all the elements of P and Q.

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

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

(ii) P ∩ Q

P ∩ Q - contains all the common elements in set P and Q.

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

P ∩ Q = {1, 2, 3, 4, 6, 12}

(iii) Q - P

Q - P - contains all the elements in set Q but not in set P.

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

Q - P = {8, 16, 24, 48}

(iv) P' ∩ Q

U is the universal set containing all the elements in set P and Q.

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

P' - contains all the elements of U which are not in P.

P' = {8, 16, 24, 48}

P' ∩ Q - contains all the common elements of P' and Q

P' ∩ Q = {8, 16, 24, 48} ∩ {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

P' ∩ Q = {8, 16, 24, 48}

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