Practical Problems on Union and Intersection of Two Sets

$E,I,R,O$ denote respectively the sets of all equilateral, isosceles, right angled and obtuse angled triangles in a plane, then which of the following is not true.

In a class of $50$ students, $10$ did not opt for math, $15$ did not opt for science and $2$ did not opt for either. How many students of the class opted for both math and science.

In a market survey you have obtained the following data which you like to examine regarding its correctness:

Asked if you will cast your vote for a party the following feedback is obtained: -

If $A=$set of Adult $C=$ Common set of Women and Youth $Y=$ set of positive opinion $N=$ set of negative opinion then $n\left(A^{\text{'}}\right)$ is

A marketing research team interviews $50$ people about their drinking habits of tea coffee or milk or $ABC$ respectively. Following data is obtained but the Manager is not sure whether these are consistent.

with the same order of options (a), (b), (c) and (d) determine the complaints about two or more than two.

The number of integers from $1$ to $1000$ which are divisible by $2$ or $3$ is

In a certain town, $25\%$ families own a phone,$15\%$ families own a car, $65\%$ families own neither a phone nor a car and $2000$ families own both a car and a phone. Consider the following Statements $\left(\mathrm{S}\right):$
$\left({\mathrm{S}}_1\right):$ $35\%$ families own at least one of a car or a phone.
$\left({\mathrm{S}}_2\right):$ $40,000$ families live in the town.
Then:

In a school there are $20$ teachers who teach Mathematics or Physics. Of these, $12$ teach Mathematics and $4$ teach both Physics and Mathematics. How many teachers teach Physics?

In a survey of $425$ students in a school, it was found that $115$ drink apple juice, $160$ drink orange juice and $80$ drink both apple as well as orange juice. How many drink neither apple juice nor orange juice?

In a survey, it was found that $21$ people liked the product $A$, $26$ liked the product $B$, and $29$ people liked the product $C$. If $14$ people liked the product $A$ and $B$, $12$ people liked the product $C$ and $A$,$14$ people liked the product $B$ and $C$ and $8$ people liked all the products. Find how many people like products $A$ and $C$ not $B$.

If $A, B, C$ are three sets and $U$ is the universal set such that $n\left(U\right)=700,n\left(A\right)=200, n\left(B\right)=300$ and $n(A\cap B)=100$. Find $n\left(A^{\text{'}}\cap B^{\text{'}}\right)$.

In a group of $20$ students, $12$ take tea, $16$ take coffee and $3$ take neither of the two. How many take both tea and coffee?

In a town of $10,000$ families, it was found that $40\%$ families buy news paper $A, 20\%$ buy news paper $B$ and $10\%$ buy newspaper $C.$ Also, $5\%$ families buy news paper $A$ and $B, 3\%$ buy news paper $B$ and $C, 4\%$ buy news paper $A$ and $C$. If $2\%$ families buy all the three newspapers, then number of families which buy news paper $A$ only is :

In a college of $300$ students, every student reads$5$ newspaper and every newspaper is read by $60$ students. The total number of newspapers is

In a class of $55$ students, the number of students studying different subjects are $23$ in Mathematics, $24$ in Physics,$19$ in Chemistry, $12$ in Mathematics and Physics, $9$ in Mathematics and Chemistry, $7$ in Physics and Chemistry and $4$ in all the three subjects. The number of students who have taken exactly one subject is

In a city $20$ percent of the population travels by car, $50$ percent travels by bus and $10$ percent travels by both car and bus. Then persons travelling by car or bus is

In a town of $10000$ families, it was found that $40\mathrm{\%}$ families buy newspaper $A,20\%$ buy newspaper $B$ and $10\mathrm{\%}$ families buy newspaper $\mathrm{C},5\%$ families buy $A$ and $\mathrm{B}, 3\%$ buy $B$ and $C$ and $4\mathrm{\%}$ buy $A$ and $C$. If $2\mathrm{\%}$ families buy all the three newspapers, then the number of families which buy $A$ only is

In a class of $60$ students, $25$ students play cricket and $20$ students play tennis and $10$ students play both the games, then the number of students who play neither is

In a certain town $25\%$ families own a cell phone, $15\%$ families own a scooter and $65\%$ families own neither a cell phone nor a scooter. If $1500$ families own both a cell phone and a scooter, then the total number of families in the town is