Sets

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A set is a collection of objects where we can definitely and clearly decide which objects belong to it. The objects in a set are called elements or members. Example: A = {1, 2, 3, 4, 5} is a set of fi…

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1. Listing Method (Roster Method): Write all elements inside curly brackets, separated by commas. Example: A = {2, 4, 6, 8} 2. Rule Method (Set Builder Form): Use a variable with a condition. Example:…

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A Singleton Set is a set that contains exactly one element. Example: A = {5} or B = {x | x is an even prime number} = {2}. These sets have only one member each.

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An Empty Set (or Null Set) is a set that contains no elements at all. It is represented by { } or φ (phi). Example: A = {x | x is a natural number between 2 and 3} = φ, because there is no natural num…

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Finite Set: A set with limited and countable number of elements. Example: A = {1, 2, 3, 4, 5} has 5 elements. Infinite Set: A set with unlimited and uncountable number of elements. Example: N = {1, 2…

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Two sets A and B are equal if every element of set A is in set B and every element of set B is in set A. Written as A = B. Example: A = {1, 2, 3} and B = {3, 1, 2} are equal sets because they have the…

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If every element of set B is also an element of set A, then B is called a subset of A. Written as B ⊆ A, read as 'B is a subset of A'. Example: If A = {1, 2, 3, 4, 5} and B = {2, 4}, then B ⊆ A becaus…

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1. Every set is a subset of itself: A ⊆ A 2. Empty set is a subset of every set: φ ⊆ A 3. If A = B, then A ⊆ B and B ⊆ A 4. If A ⊆ B and B ⊆ A, then A = B…