Question

Let $A=\left\{1,2,3,4\right\}$ $,$ $B=\left\{a,b,c,d\right\}$ and $C=\left\{x:x<5,x\in N\right\}$. State which of the following is true and which is false$.$

$B\leftrightarrow C$

• A. True
• B. False

Answer 1

The correct option is A True

The given sets are $A=\left\{1,2,3,4\right\}$

$B=\left\{a,b,c,d\right\}$ and $C=\left\{x:x<5,x\in N\right\}$

$C=\left\{x:x<5,x\in N\right\}$ in Roster form can be defined as follows

In the set $C$ elements are natural number and less than $5$

$C=\left\{1,2,3,4\right\}$

Number of elements in the given sets $A,B$ and $C$ are given below

$n\left(A\right)=4,n\left(B\right)=4,n\left(C\right)=4$

Two or more than two sets are said to be equivalent sets iff number of elements are equal$.$

Two equivalent sets are denoted by $\leftrightarrow$ symbol

Number of elements in sets $B$ and $C$ are equal$.$

$B\leftrightarrow C$

Hence$,$ the given statement $B\leftrightarrow C$ is true.