Mathematics
Let P and Q be two sets such that n(P ∪ Q) = 70, n(P) = 45 and n(Q) = 38. Draw a Venn diagram and find :
(i) n(P ∩ Q)
(ii) n(P - Q)
(iii) n(Q - P)
Answer
Given:
n(P ∪ Q) = 70
n(P) = 45
n(Q) = 38
(i) n(P ∩ Q)
To find the number of elements in the intersection, we use the formula:
n(P ∪ Q) = n(P) + n(Q) - n(P ∩ Q)
Rearranging to solve for the intersection:
n(P ∩ Q) = n(P) + n(Q) - n(P ∪ Q)
Substituting the values in above, we get:
n(P ∩ Q) = 45 + 38 - 70
n(P ∩ Q) = 83 - 70
∴ n(P ∩ Q) = 13
(ii) n(P - Q)
This represents elements that are in set P but not in set Q.
We use the formula:
n(P - Q) = n(P) - n(P ∩ Q)
Substituting the values in above, we get:
n(P - Q) = 45 - 13
∴ n(P - Q) = 32
(iii) n(Q - P)
This represents elements that are in set Q but not in set P.
We use the formula:
n(Q - P) = n(Q) - n(P ∩ Q)
Substituting the values in above, we get:
n(Q - P) = 38 - 13
∴ n(Q - P) = 25
Related Questions
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