The Boolean Logic of Set Intersections
Read this topicExplanations 3
- The intersection of two sets contains those elements that are in both sets. We write the intersection of set A and set B as A∩BA\cap BA∩B. The intersection of many sets contains…
By Elena Koslover
- An intersection is an operation between two sets. If these sets are AAA and BBB, then the intersection of the two sets is a set itself, the set containing all elements in both A…
By Joshua Siktar
- can be calculated as .
By Hyunwoo (David) Lee
Problems 7
- Simplify the following expression: ((x∈A)∧(x∈B)∧(x∉C))∨((x∈A)∨(x∈B))((x \in A) \land (x \in B) \land (x \notin C)) \lor ((x \in A) \lor (x \in B))((x∈A)∧(x∈B)∧(x∈/C))∨((x∈A)∨(x∈B))
- What is the minimum number of elements in the union of two sets whose intersection consists of exactly five elements?
- What is the intersection of R\mathbb{R}R (set of real numbers) and C\mathbb{C}C (set of complex numbers)?
- Let A={1,4,−2,27}A = \{1, 4, -2, 27\}A={1,4,−2,27}. Which of the following statements about set intersections are true?
- xxx and yyy are real numbers such that {2x,3x}∩{x2}={y}\{2x, 3x\} \cap \{x^2\} = \{y\}{2x,3x}∩{x2}={y}. What is the largest possible value of yyy?
- Let AAA and BBB be sets. Which of the following are always true?
- Let AAA, BBB, and CCC be sets. Which of the following are always true?