Question

{x : x is a circle in the plane} _____ {x : x is a circle in the same plane with radius 1 unit} Make correct statement by filling in the symbols $\subset or \not \subset$. in the blank space.

Answer 1

we know, A set is known as subset of another set if all elements of the set are elements of the set. for example :- set A = {a, e, i} and set B = {a, b, c , d , e , f , g , h , i} are given then, we can say set A is subset of set B, because all elements of set A are elements of set B. hence, we can write it $A\subset B$.

now come to the question,
here, first set has no fixed radius of circles whereas the second set has only circles with radius 1 unit. hence, {x : x is a circle in the plane}$\not\subset$ {x : x is a circle in the same plane with radius 1 unit}