Question

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

Answer 1

(i)

Since every element of { 2,3,4 } is contained in { 1,2,3,4,5 }, so,

{ 2,3,4 }⊂{ 1,2,3,4,5 }

(ii)

Since all the elements of { a,b,c } are not contained in { b,c,d }, so,

{ a,b,c }⊄{ b,c,d }

(iii)

Since all the students of class XI of one school are contained in that school, so,

{ x:x is a student​of​class XI of your school }⊂{ x:x is student of your school }

(iv)

Since all the circles in a plane are not contained in the set of circles in the same plane with radius 1 unit, so,

{ x:x is a circle in the plane }⊄{ x:x is a circle in the same plane with radius 1 unit }

(v)

Since the triangles in a plane is not the rectangle in that plane, so,

{ x:x is a triangle in a plane }⊄{ x:x is a rectangle in a plane }

(vi)

Since all the equilateral triangles in a plane are contained in the set of all the triangles in a plane, so,

{ x:x is an equilateral triangle in the plane }⊂{ x:x is a triangle in the same plane }

(vii)

Since all the even natural numbers are also integers, so,

{ x:x is an even natural number }⊂{ x:x is an integer }