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By Pulgarin A.

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Universal quantifier, which is denoted by ∀ and means for every, for any. 2. Existential quantifier, which is denoted by ∃ and means there exists (at least one), there is (at least one). 8 • ∃ x ∈ {1, 2, 3} such that x is an even number. • ∀ set A ∃ set B such that A = B. 2 Subset If all the elements of a set B belong to a set A, then B is called a subset of A (Fig. , B ⊆ A ⇔ (∀x ∈ B Ÿ x ∈ A). 1) A B Fig. 1. Visualization of the notion of subset, B ⊂ A. , all the elements of B belong to A, but A also has other elements: B ⊂ A ⇔ ((∀x ∈ B Ÿ x ∈ A) ȁ (∃y ∈ A Ÿ y ∉ B)).

Bn} denotes a set of Web pages (or books). ,Tm denote the terms appearing in them. Create a partition P of set B if all the pages (books) in which the term Ti has the same number of occurrences are equivalent to each other. ,m. What do you observe? 9. ,Bn denote all the Web pages of the World Wide Web, or all the books held in a library. Do they form a set? : History of Logic (Abacus Press, Kent, 1977) Enderton, H. : A Mathematical Introduction to Logic (Academic Press, New York, 1972) Halmos, P.

The structure (L, ∧, ∨) is called a lattice if the following properties hold: • Commutativity: • Associativity: • Absorption: A ∧ B = B ∧ A, A ∨ B = B ∨ A, ∀A, B ∈ L. A ∧ (B ∧ C) = (A ∧ B) ∧ C, ∀A, B, C ∈ L. A ∨ (B ∨ C) = (A ∨ B) ∨ C, ∀A, B, C ∈ L. A ∧ (A ∨ B) = A, A ∨ (A ∧ B) = A, ∀A, B ∈ L. It is worth noting that: 1. First, absorption is the only property that connects the meet and the join. 2. Second, any lattice L is at the same time a commutative semigroup with respect to the meet and the join (a semigroup is a structure (G, *) in which the operation * is associative).

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A Characterisation of Ck(X) As a Frechet f-Algebra by Pulgarin A.


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