Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
{2, 3, 4} ... {1, 2, 3, 4, 5}
{2, 3, 4} ⊂ {1, 2, 3, 4, 5}
{a, b, c} ... {b, c, d}
{a, b, c} ⊄ {b, c, d}
{x : x is a student of Class XI of your school} ... {x : x student of your school}
{x : x is a student of Class XI of your school} ⊂ {x : x student of your school}
{x : x is a circle in the plane} ... {x : x is a circle in the same plane with radius 1 unit}
{x : x is a circle in the plane} ⊄ {x : x is a circle in the same plane with radius 1 unit}
{x : x is a triangle in a plane} ... {x : x is a rectangle in the plane}
{x : x is a triangle in a plane} ⊄ {x : x is a rectangle in the plane}
{x : x is an equilateral triangle in a plane} ... {x : x is a triangle in the same plane}
{x : x is an equilateral triangle in a plane} ⊂ {x : x is a triangle in the same plane}
{x : x is an even natural number} ... {x : x is an integer}
{x : x is an even natural number} ⊂ {x : x is an integer}
Explanation
This question tests understanding of subset relationships. A set A is a subset of set B (A ⊂ B) if every element of A is also an element of B. If even one element of A is not in B, then A ⊄ B. In parts (i), (iii), (vi), and (vii), all elements of the first set belong to the second set, making them proper subsets. In parts (ii), (iv), and (v), the first set contains elements not present in the second set, so the subset relation does not hold.