132
Subsets
Textbook: Part 4, lesson 132, pp. 69–71
GoalSubsets: the sign B ⊂ A, deciding whether one set is a subset of another.
New words
subset · qismto‘plamis included in · kiradithe sign ⊂ · belgi ⊂all the elements · barcha elementlar
Explanation
If all the elements of the set B are also in the set A, then B is a subset of A and we write B ⊂ A. If at least one element of B is not in A, then B ⊄ A. In a diagram a subset is a small oval inside a big oval.
Worked examples
A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, B = {2, 4, 6, 8}. Every element of B is in A, so B ⊂ A.
Let C = {3, 5, 11}. The number 11 is not in A, so C ⊄ A. From life: the set of girls in a class is a subset of the set of all pupils of the class.
Class activity
“Subset cards”: the teacher shows cards “animals”, “birds”, “snakes”, “fruits”. Pairs of children decide which set is a subset of which.
Practice
1
A = {1, 2, 3, 4, 5}, B = {2, 5}. Is B ⊂ A?
Yes, B ⊂ A: both 2 and 5 are in A.
2
A = {1, 2, 3, 4, 5, 6, 7, 8, 9}, C = {2, 4, 10}. Is C ⊂ A?
No, 10 ∉ A, so C ⊄ A.
3
Is the set of squares a subset of the set of quadrilaterals?
Yes, every square is a quadrilateral.
4
Write the two-element subsets of A = {a, b, c}. How many are there?
3: {a, b}, {a, c}, {b, c}
5
Of the set of animals and the set of snakes, which is a subset of the other?
The set of snakes is a subset of the set of animals.