Sets and Their Representations

Let
$\mathrm{X}=\{\mathrm{x}\mid \mathrm{x}=2+4\mathrm{k}$, where $\mathrm{k}=0,1,2,3,\dots 24\}$.
Let $S$ be a subset of $X$ such that the sum of no two elements of $S$ is $100$ . What is the maximum possible number of elements in $S$ ?

In a party of $150$ persons, $75$ persons take tea, $60$ persons take coffee and $50$ persons take milk. $15$ of them take both tea and coffee, but no one taking milk takes tea. If each person in the party takes at least one drink, then what is the number of persons taking milk only?

What is a set ?

How many number from $1 to 50$ neither divible by $3 nor 5?$

In a survey, $45$ people found who like to work on laptop, $30$ people. Who liked to work on PC and $10$ people an comfortable with both. Find how many people are there who liked to worth, manually if $100$ people are surveyed?

If a set contains $4$ elements the number of subsets formed by this set is

How many numbers from $1 to 50$ neither divisible by $3 nor 5?$

For how many ordered pairs of positive integers $(\mathrm{x}, \mathrm{y}) \mathrm{is} \mathrm{x} + 2\mathrm{y} = 100$?

If $P\left(A\right)=\frac{2}{3},P\left(B\right)=\frac{3}{8},P\left(A\cap B\right)=\frac{1}{4}$, then events $A\&B$ are.......

In the universal set U: set of all natural numbers below$500$: Set A consists of all odd numbers below $100$. Set B consists of all multiples of $2$less than $200$, Set C consists of all multiples of $7$less than $500$. How many elements are there in the set in $\left\{\mathrm{A}\cup (\mathrm{B}\cup \mathrm{C}’)\right\}$?

find the number of workers in set $L\cap I.$

Consider the following data : -

If S M L T I denote short medium long terms skilled and indirect workers respectively find the number of workers in set $M.$

with the same order of options (a) (b) (c) and (d) how many buy C and B grades but not the A grade ?

with the same order of options (a) (b) (c) and (d) how many buy C grade if and only if they do not buy B grade?

with the same order of options (a), (b), (c) and (d) the set $n(A\cap C)$ is

If $V=\{0,1,2,\dots 9\},X=\{0,2,4,6,8\},Y=\{3,5,7\}$ and $Z=\left\{37\right\}$ then $Y\cup Z,( V\cup Y)\cap X,(X\cup Z)\cup V$ are respectively:-

Which of the diagram is graph of a function

Which of the following statements is false?

The two sets $\mathrm{x}$ and $\mathrm{y}$ are defined as $\mathrm{x}=\left\{{\mathrm{a}}^{\mathrm{b}}-\mathrm{b}\right.,$ where $\mathrm{a}=$ even and $\mathrm{b}=$ odd positive integers $\}$ and $\mathrm{y}=\{\mathrm{a}\times \mathrm{b};$ for $\mathrm{a}=1,2,3,4\dots \dots .$ and $\mathrm{b}=$ prime number $\},$ then which of the following is true?

Everybody, in a class of$30$ students plays at least one of the games between cricket and football. $16$ students play football. There are 7 students who play football but do not play cricket. Find the difference between the number of students who play both the game and the number of students who play cricket only.