Question 651
CBSE Class 11 Mathematics · Sets · Subsets, intervals and universal sets
Insert \(\subset\) or \(\not\subset\) between each pair:
- \(\{2,3,4\}\), \(\{1,2,3,4,5\}\)
- \(\{a,b,c\}\), \(\{b,c,d\}\)
- Class XI students of your school, all students of your school
- all circles in a plane, unit circles in that plane
- triangles in a plane, rectangles in that plane
- equilateral triangles in a plane, all triangles in that plane
- even natural numbers, integers
Solution to Question 651
Complete workingA set is a subset only when every element of the first belongs to the second. Applying this test gives:
\[\subset,\ \not\subset,\ \subset,\ \not\subset,\ \not\subset,\ \subset,\ \subset.\]
For example, a circle of radius 2 disproves (iv), while every equilateral triangle is certainly a triangle.
Final results
1
(i) \(\subset\)
2
(ii) \(\not\subset\)
3
(iii) \(\subset\)
4
(iv) \(\not\subset\)
5
(v) \(\not\subset\)
6
(vi) \(\subset\)
7
(vii) \(\subset\).