Let A and B are the subsets of the universal set U. Let $\mathrm{n}\left(\mathrm{A}\right)=20, \mathrm{n}\left(\mathrm{B}\right)=30, \mathrm{n}\left(\mathrm{U}\right)=80$ and $\mathrm{n}(\mathrm{A}\cap \mathrm{B})=10$. Then $\mathrm{n}({\mathrm{A}}^{\text{'}}\cap {\mathrm{B}}^{\text{'}})=\mathrm{\_\_\_\_\_}$

Among 50 patients admitted to a hospital, 25 are diagnosed with pneumonia, 30 with bronchitis and 10 with both pneumonia and bronchitis. Then the number of patients not diagnosed with pneumonia or bronchitis.

A survey in 1986 asked households, whether they had a VCR, a CD player or cable TV. 40 had a VCR, 60 had a CD player and 50 had a cable TV. 25 had VCR and CD player. 30 had CD player and cable TV. 35 had VCR and cable TV. 10 households had all three. How many households had at least one of the three?

Among 18 students in a classroom, 7 study Mathematics, 10 study Science and 10 study Computer programming. Also, 3 study Mathematics and Science, 4 study Mathematics and Computer programming and 5 study Science and Computer programming. We know that 1 student studies all three subjects. How many of these students study none of the three subjects?

If n(A)=n then how many elements in the power set of A?

If A={1,2} and B={a,b} then A$\times$B=_____.

If A has m elements and B has n elements then A$\times$B has _____ elements.

Let A = {1,2,3,4} then (1). n(A) = _____. (2). n(P(A)) = _____. (3). No. of proper subsets of A = _____. (4). No. of improper subsets of A = _____.

$\mathrm{If} \mathrm{A}\cap \mathrm{B}=\mathrm{\varphi } \& \mathrm{A}\cup \mathrm{B}=\mathrm{U}. \mathrm{Then} {\mathrm{A}}^{\text{'}}=\mathrm{\_\_\_\_\_}.$

If n(A)=m and n(B)=n, then how many different functions from A to B?