Open sentences, subsets and the laws of sets
Tell statements from open sentences, build the solution set of an open sentence, count subsets, and check the distributive and absorption laws on a Venn diagram.
- Iran: grade 11
- Palestine: grade 11
- Russia: grade 8
Guide
This studio follows Iran's Grade 11 Statistics and Probability, chapter 1: open sentences (گزارهنما) and the algebra of sets.
A sentence with a variable, such as x + 2 > 5, is neither true nor false until x has a value: it is an open sentence. The values x may take are its domain. Each value turns it into a statement.
A set with n elements has 2n subsets: each element is in or out. A ⊆ B means every element of A is in B, and to prove it we take an arbitrary x in A and show x is in B. Two sets are equal when each is a subset of the other.
To check a law such as the distributive law, shade each side on the same Venn diagram and see that the regions match.