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

(iv) {x : x is a student of I PUC of your college} … {x : x is student of your college}. 

(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) {2, 3, 4} ⊂ {1, 2, 3, 4, 5} 

∵ 2, 3, 4 ∈ {1, 2, 3, 4, 5} 

(ii) {a, b, c} ⊄ {b, c, d} 

∵ a ⊄ {b, c, d} 

(iii) {x: x is a circle in the plane} ⊄ {x: x is a circle in the same plane with radius 1 unit}. Because there exists a circle having a radius other than 1 unit. 

(iv) {x: x is a student of 1 PUC of your college} ⊄ {x: x is a student of your college} 

∵ Every student of I PUC is a student of the college. 

(v) {x: x is a triangle in a plane} ⊄ {x: x is a rectangle in the plane. 

∵ Triangle is not a rectangle. 

(vi) {x: x is an equilateral triangle in a plane} ⊂ {x: x is a triangle in the same plane}. 

∵ Every equilateral triangle in a plane is a triangle in the same plane. 

(vii) {x : x is an even natural number} ⊂ {x : x is an integer} 

∵ Every even natural number is an integer.