Mathematics
If P = {x : x ∈ W and 4 ≤ x ≤ 8} and Q = {x : x ∈ N and x < 6}. Find
(i) P ∪ Q and P ∩ Q.
(ii) Is (P ∪ Q) ⊃ (P ∩ Q) ?
Sets
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Answer
P = {x : x ∈ W and 4 ≤ x ≤ 8}
P = {4, 5, 6, 7, 8}
Q = {x : x ∈ N and x < 6}
Q = {1, 2, 3, 4, 5}
(i) P ∪ Q - contains all the elements in both sets P and Q.
P ∪ Q = {4, 5, 6, 7, 8} ∪ {1, 2, 3, 4, 5}
P ∪ Q = {1, 2, 3, 4, 5, 6, 7, 8}
P ∩ Q - contains all the common elements in both sets P and Q.
P ∩ Q = {4, 5, 6, 7, 8} ∩ {1, 2, 3, 4, 5}
P ∩ Q = {4, 5}
(ii) From (i) we can clearly see that every elements in P ∩ Q is also in P ∪ Q.
Hence, (P ∪ Q) ⊃ (P ∩ Q) is correct.
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