MATH 2420 Discrete Mathematics
... 2. Inclusion in Union: For all sets A and B, A ⊆ A ∪ B and B ⊆ A ∪ B 3. Transitive Property of Subsets: For all sets A, B, and C if A ⊆ B and B ⊆ C, then A ⊆ C Procedural Versions of Set Definitions Let X and Y be subsets of a universal set U and suppose x and y are elements of U . ...
... 2. Inclusion in Union: For all sets A and B, A ⊆ A ∪ B and B ⊆ A ∪ B 3. Transitive Property of Subsets: For all sets A, B, and C if A ⊆ B and B ⊆ C, then A ⊆ C Procedural Versions of Set Definitions Let X and Y be subsets of a universal set U and suppose x and y are elements of U . ...
STD VII - Kerala Samajam Model School
... Identify finite, infinite, empty and the singleton sets among the following: a. Set of odd numbers divisible by 2 b. Set of even prime numbers c. { x: x is right angle in an acute angled triangle} d. The set of positive integers greater than 100 e. { x:x is an obtuse angle in a scalene triangle} ...
... Identify finite, infinite, empty and the singleton sets among the following: a. Set of odd numbers divisible by 2 b. Set of even prime numbers c. { x: x is right angle in an acute angled triangle} d. The set of positive integers greater than 100 e. { x:x is an obtuse angle in a scalene triangle} ...
BASIC SET THEORY
... Sets can be finite or infinite. (A rigorous definition of "finite set" will have to wait, but our intuition should be adequate here.) Every finite set has a cardinality or size. This is often written as |S| or #(S). For finite sets this is just the number of elements. THEOREM: Two finite sets have ...
... Sets can be finite or infinite. (A rigorous definition of "finite set" will have to wait, but our intuition should be adequate here.) Every finite set has a cardinality or size. This is often written as |S| or #(S). For finite sets this is just the number of elements. THEOREM: Two finite sets have ...
Indexed Collections Let I be a set (finite of infinite). If for each
... Let I be a set (finite of infinite). If for each element i of I there is an associated object xi (exactly one for each i) then we say the collection xi , i ∈ I is indexed by I. Each element i ∈ I is called and index and I is called the index set for this collection. The definition is quite general. Usu ...
... Let I be a set (finite of infinite). If for each element i of I there is an associated object xi (exactly one for each i) then we say the collection xi , i ∈ I is indexed by I. Each element i ∈ I is called and index and I is called the index set for this collection. The definition is quite general. Usu ...
3-8 Unions and Intersection of Sets
... In your left pocket, you have a quarter, a paper clip, and a key. In your right pocket, you have a penny, a quarter, a pencil, and a marble. What is a set that represents the different items in your pockets ...
... In your left pocket, you have a quarter, a paper clip, and a key. In your right pocket, you have a penny, a quarter, a pencil, and a marble. What is a set that represents the different items in your pockets ...
Lecture notes 2 -- Sets
... of B. Some texts use two di↵erent symbols to indicate the property of being a subset, and the property of being a proper subset. More specifically, if A is a proper subset of B, then they will write A ⇢ B; if A might be equal to B, then they will write A ✓ B. Other books use these two terms intercha ...
... of B. Some texts use two di↵erent symbols to indicate the property of being a subset, and the property of being a proper subset. More specifically, if A is a proper subset of B, then they will write A ⇢ B; if A might be equal to B, then they will write A ✓ B. Other books use these two terms intercha ...
