Mathematics
If P = {factors of 36} and Q = {factors of 48} ; find :
(i) P ∪ Q
(ii) P ∩ Q
(iii) Q - P
(iv) P' ∩ Q
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}
Related Questions
Given A = {0, 1, 2, 4, 5}, B = {0, 2, 4, 6, 8} and C = {0, 3, 6, 9}. Show that :
(i) A ∪ (B ∪ C) = (A ∪ B) ∪ C, i.e., the union of sets is associative.
(ii) A ∩ (B ∩ C) = (A ∩ B) ∩ C, i.e., the intersection of sets is associative.
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Name the sets which are equal.
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(i) A - B
(ii) B - C
(iii) B - (A - C)
(iv) A - (B ∪ C)
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