Sets Test - 46...

In \(\mathrm{n}(\mathrm{A})=20, \mathrm{n}(\mathrm{B})=35\) and \(\mathrm{n}(\mathrm{A} \cup \mathrm{B})=45\), then \(\mathrm{n}(\mathrm{A} \cap \mathrm{B})\) equals:

Given the sets \(\mathrm{A}=\{2,3,4,5,6,7\}, \mathrm{B}=\{6,7,8\}\) and \(\mathrm{C}=\{1,5,8,9\}\) then find \(A \cap(B \cup C)\) and number of elements in \(A \cap(B \cup C)\)

In a group of 70 persons, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like coffee but NOT tea?

Write the set builder form for \(D=\{-6,-4,-2,0,2,4,6\}\).

If \(A=\{a, b, c, d, e\}, B=\{a, c, e, g\}\) and \(C=\{b, e, f, g\} .\) Find \((A \cup B) \cap(A \cup\) C)?

Let \(X=\{1,2,3,4,5\}\). The number of different ordered pairs \((Y, Z)\) that can be formed such that \(Y \subseteq X, Z \subseteq X\) and \(Y \cap Z\) is empty, is:

Let \(\mathrm{n(U)=42, n(X)=15, n(Y)=12}\) and \(\mathrm{n(X \cup Y)=22}\), then find cardinality of the shaded region in the below-given Venn diagram.

Let \(S=\{1,2,3, ....., 100\}\). The number of non-empty subsets \(A\) of \(S\) such that the product of elements in \(A\) is even is:

Write the set builder form for \(B=\{1000,1331,1728,2197, 2744, 3375, \ldots, 8000\}\).

Sets \(A\) and \(B\) have 5 and 7 elements respectively. What will be the minimum number of elements in \(A \cup B\)?