Suppose that in a certain exam, $200$ students appear for Mathematics, $50$ appear for physics, $100$ appear for Chemistry, $20$ appear for Mathematics & Physics, $60$ appear for Mathematics & Chemistry, $35$ appear for Physics & Chemistry, while $245$ appear for either Mathematics or Physics or Chemistry.

Determine the number of students who appear for

(i) All 3 subjects

(ii) Exactly for one of the subjects

Use Venn Diagram to find the same.

Let $\underset{i=1}{\overset{50}{\cup }}{X}_i=\underset{i=1}{\overset{n}{\cup }}{Y}_i=T$, where each $X_i$ contains $10$ elements and each $Y_i$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets $X_i$'s and exactly $6$ of sets $Y_i$'s then $n$ is equal to :

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

Let $S_1, S_2$ and $S_3$ be three sets defined as

$S_1=\{z\in ℂ:|z-1|\le \sqrt{2}\},$

$S_2=\{z\in ℂ:Re((1-i)z)\ge 1\}$ and

$S_3=\{z\in ℂ:Im(z)\le 1\}.$

Then, the set $S_1\cap S_2\cap S_3$