Set theory: Mathematical logic and proving techniques

• A set is any collection of objects with similar characteristics
• Null set or empty set (ø or { }) is a set without any elements.
• Universal set is defined as set consisting of all elements under consideration,
symbolic in U or ξ.
• Subset for example A ⊂ B if and only if x ϵ A and x ϵ B.
1. Improper subset (⊆): if there is possibility that A = B and A is totally included in B.
2. Proper subset (⊂): element in set A must be less than element in set B

• Ø ϵ Ø false
• Ø ⊂ Ø false
• Ø ⊆ Ø true
• Ø ϵ {Ø} true
• Ø ⊂ {Ø} true
• Ø ⊆ {Ø} true

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