Question

Make correct statements by filling in the symbols $\subset$ or $\subset ̸$ in the blank spaces:
$\left(i\right)\{2,3,4\}...\{1,2,3,4,5\}$
$\left(ii\right)\{a,b,c\}...\{b,c,d\}$
$\left(iii\right)\{x:x$ is a student of class $XI$ of your school$\}...\{x:x$ is a student of your school}
$\left(iv\right)\{x:x$ is a circle in the plane$\}...\{x:x$ is a circle in the same plane with radius $1$ unit$\}$
$\left(v\right)\{x:x$ is a triangle in a plane} {$x:x$ is a rectangle in the plane}
$\left(vi\right)\{x:x$ is an equilateral triangle in a plane$\}...\{x:x$ is a triangle in the same plane$\}$
$\left(vii\right)\{x:x$ is an even natural number$\}...\{x:x$ is an integer$\}$

Answer 1

$\left(i\right)$ Let $A=\{2,3,4\}$ and $B=\{1,2,3,4,5\}$
$\because$ Every element of set $A$ is belonging to set $B$.
$\therefore A\subset B$
$\{2,3,4\}\subset \{1,2,3,4,5\}$

$\left(ii\right)a\in \{a,b,c\}$ but $a\notin \{b,c,d\}$
$\therefore \{a,b,c\}\subset ̸\{b,c.d\}$

$\left(iii\right)\because$ Student of class $XI$ belongs to given school,
$\therefore \{x:x$ is a student of class $XI$ of your school$\}\subset \{x:x$ is a student of your school$\}$

$\left(iv\right)\because$ Circle in a plane can be of any radius, not only of $1$ unit,
$\therefore \{x:x$ is a circle in the plane$\}\subset ̸\{x:x$ is a circle in the same plane with radius $1$ unit$\}$

$\left(v\right)$ Since a triangle cannot be equal to a rectangle,
$\therefore \{x:x$ is a triangle in a plane$\}\subset ̸\{x:x$ is a rectangle in the plane$\}$

$\left(vi\right)$ Since every equilateral triangle is a triangle,
$\therefore \{x:x$ is a equilateral triangle in a plane$\}\subset \{x:x$ is a triangle in the same plane}

$\left(vii\right)$ Let $A=$ {$x:x$ is an even natural number} and $B=$ {$x:x$ is an integer}
$\therefore A=\{2,4,6,...\}$ and $B=\{...,-2,-1,0,1,2,3,4,5,...\}$
$\therefore A\subset B$
Alternatively.
Since all even natural numbers are integers,
$\therefore \{x:x$ is an even natural number$\}\subset \{x:x$ is an integer$\}$