Question
Download Solution PDFComprehension
Directions: Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z). which is equal to 90.
If the number of elements belonging to neither X, nor Y, nor Z is equal to p, then what is the number of elements in the complement of X?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Complement of X = U - X, where U is a universal set.
Calculation:
We know, n(X) + n(Y) + n(Z) - n(X ∩ Y) - n(Y ∩ Z) - n(X ∩ Z) + n(X ∩ Y ∩ Z) = n(X ∪ Y ∪ Z)
Here U - n(X ∪ Y ∪ Z) = p, whre U is a universal set
⇒ U - (a + b + 106) = p
⇒ U = p + (a + b + 106)
Now the number of elements in the complement of X, U - n(X) = p + (a + b + 106) - (a + 16 + 18 + 12)
= p + b + 60
Hence, option (1) is correct.
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