Disjoint Sets

Q. Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y,Z)$ that can be formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is

1. $5^3$
2. $5^2$
3. $3^5$
4. $2^5$

Q. Which of the following pairs of sets are disjoint?
$\left(i\right)\{1,2,3,4\}\text{and}\{x:x\text{is a natural number and}4\le x\le 6\}$
$\left(ii\right)\{a,e,i,o,u\}\text{and}\{c,d,e,f\}$
$\left(iii\right)\{x:x\text{is an even integer}\}\text{and}\{x:x\text{is an odd integer}\}$

Q. If $S$ and $T$ are two sets such that $S$ has $21$ elelments, $T$ has $32$ elements and $S\cap T$ had $11$ elements, how many elements does $S\cup T$ have?

Q. State which of the following pairs of sets are disjoint :

ii. {birds} and {trees}

Q. If two sets A and B have no common elements, i.e. $A\cap B$ has no elements, such sets are known as _____________.

1. Intersection
2. Union
3. Disjoint
4. Complement

Q.

State, which of the following pairs of sets are disjoint :

v:- {people living in Calcutta} and

{people living in west Bengal}

Q. Given three sets $A,B\&C$such that $A\subset B$ and $B\&C$ are disjoint sets, then the correct representation of the three sets is:

1. 
2. 
3. 
4. 

Q. State whether each of the following statement is true or false. Justify your answer.
$\left(i\right)\{2,3,4,5\}$ and $\{3,6\}$ are disjoint sets.
$\left(ii\right)\{a,e,i,o,u\}$ and $\{a,b,c,d\}$ are disjoint sets.
$\left(iii\right)\{2,6,10,14\}$ and $\{3,7,11,15\}$ are disjoint sets.
$\left(iv\right)\{2,6,10\}$ and $\{3,7,11\}$ are disjoint sets.

Q. Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y,Z)$ that can be formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is

1. $5^3$
2. $5^2$
3. $3^5$
4. $2^5$

Q. State, which of the following pairs of sets are disjoint :

{$x:x$ is a fan of cricket} and {$x:x$ is a fan of football}

Q. If $A$ is the set of people who travel only by bus, $B$ is the set of people who travel only by car, then which of the following will be the correct representation?

1. 
2. 
3.