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 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?

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 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

There are $600$ boys in a hostel. Each plays either hockey or football or both. If $75\%$ play hockey and $45\%$ play football, how many play both?

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

If $X$ and $Y$ are two sets such that $X$ has $40$ elements, $X\mathit{\cup }Y$ has $60$ elements and $X\mathit{\cap }Y$ has $10$ elements, how many elements does $Y$ have ?