Tag: introduction to set

In a group of $760$ persons, $510$ can speak Hindi and $360$ can speak English. Find how many can speak Hindi only.

There are $25$ trays on a table in the cafeteria. Each tray contains a cup only, a plate only, or both a cup and a plate. If $15$ of the trays contain cups and $21$ of the trays contain plates, how many contain both a cup and a plate?

Let A = {x : x is a square of a natural number and x is less than 100} and B is a set of even natural numbers. What is the cardinality of $ A \cap B$ ?

If $A = ${1,4,6}, $B = ${3,6}, then find $(A \cap B)$

$If\ A = {1, 2, 3}, B = {4, 5}, then\ find\ A \cap B$

A survey shows that $63\%$ of Indians like mangoes whereas $76\%$ like apple. If $x%$ of the Indians like both mangoes and apples, then

Two set A and B are as under 
A = {(a,b) $\epsilon$ R $\times$ R : $\mid a - 5\mid$ < $1$ and  $\mid b - 5\mid$ < $1$};
B = {(a,b) $\epsilon$ R $\times$ R : $4(a-6)^2 + 9(b-5)^2$ $\leq 36$. Then, 

$R$ is the set of all positive odd integers less than $20$; $S$ is the set of all multiples of $3$ that are less than $20$. How many elements are in the set $R$ $\cap$ $S$?

Let $Z$ denotes the set of all integers and $A=\left{ \left( a,b \right) :{ a }^{ 2 }+3{ b }^{ 2 }=28,a,b\in Z \right} $ and $B=\left{ \left( a,b \right) :a < b,a,b\in Z \right} $. Then, the number of elements in $A\cap B$ is

Let $A,B$ be two sets such that $A\cap B=\phi$, then $A=\phi$ and $B=\phi$?