Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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I need you to write me the answers on paper. For 1. Expand in two object universe (the objects are named ‘a’ and ‘b’) For part 2. Indicate which variables are free and which are bound ( you can use ‘F’ for free and ‘B’ for bound). Either (i) draw a vertical line underneath each variable with the letters ‘F’ or ‘B’ at the bottom of each vertical line or (in) color bound variables red and free variables green.
1. Expand in a two-object universe (the objects are named 'a' and 'b')
(a) (Ex) ((Ax Bd) = Dy)
(b)(x) (Ax & Cz)
(c) (x) (Dy (Hx & -Ga))
Expanding a wff is not the same as reducing the wff to conjunctive normal form (or reducing it to disjunctive normal form). Read the text and my handout on how
to do an expansion.
I
2. For the following wffs, indicate which variables are free and which are bound (you can use 'F' for free and 'B' for bound.) Either (i) draw a vertical line
underneath each variable with the letters 'F' or 'B' at the bottom of each vertical line or (ii) color bound variables red and free variables green. Make sure you
know which symbols are used for variables. Not every symbol in the language of predicate logic is used for variables. The reading (Scope, binding, and quantifier
expansions) lists the symbols that are used for variables and the symbols that used for the names of objects (i.e., individual constants). Names of objects are not
names of variables. The free/bound distinction only applies to variables. It does not apply to individual constants (i.e., names of objects)
(a)
(b)
(c)
(x) (y) (Ez) ((Ayzxv Bzzy) v (Fxac
Hzauzu))
(Ex) (Ey) Hyabwa (z) (Fzvhky v Hxyyx)
(z) (Ex) (y) (Axyzyyw v Bxyxzavz)
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Transcribed Image Text:1. Expand in a two-object universe (the objects are named 'a' and 'b') (a) (Ex) ((Ax Bd) = Dy) (b)(x) (Ax & Cz) (c) (x) (Dy (Hx & -Ga)) Expanding a wff is not the same as reducing the wff to conjunctive normal form (or reducing it to disjunctive normal form). Read the text and my handout on how to do an expansion. I 2. For the following wffs, indicate which variables are free and which are bound (you can use 'F' for free and 'B' for bound.) Either (i) draw a vertical line underneath each variable with the letters 'F' or 'B' at the bottom of each vertical line or (ii) color bound variables red and free variables green. Make sure you know which symbols are used for variables. Not every symbol in the language of predicate logic is used for variables. The reading (Scope, binding, and quantifier expansions) lists the symbols that are used for variables and the symbols that used for the names of objects (i.e., individual constants). Names of objects are not names of variables. The free/bound distinction only applies to variables. It does not apply to individual constants (i.e., names of objects) (a) (b) (c) (x) (y) (Ez) ((Ayzxv Bzzy) v (Fxac Hzauzu)) (Ex) (Ey) Hyabwa (z) (Fzvhky v Hxyyx) (z) (Ex) (y) (Axyzyyw v Bxyxzavz)
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