Question 1 In this exercise use the transformation rules given in the picture uploaded, to verifythat the following are formulas of quantified relational logic.(a) Ba (b) ¬Bb (c) ∃x¬Bx (d) ∃x(Rx ∧ ¬Bx) (e) ¬∀x(Rx → Bx) (f) ((Rb ∧ ¬Bb) → ∃x(Rx ∧ ¬Bx)) (The image shows rules and formulas if your not familiar with this) We are now in a position do describe quantified relational logicfor one or two place relations only. Remember that to specify alogic I need to tell you (1) the formal symbols, (2) thetransformation rules, and (3) closure condition.The formal symbols are:· a, b, c, . . . , m, n, . . . as constant symbols for terms. A term isanything in a theory or language that can be given a propername or an object that can be identified uniquely.- x, y, z as symbols for variables, which range over terms.- Upper case letters P, Q, R, S, T, . . . , A, B, C, D, . . . , M, . . . ofalphabet as symbols for relations (on two placetheonly).- Truth-functional connectives: V, ^, , , ↔- Quantifiers: V- Brackets: ( for left bracket and ) for right bracket.In order to talk about formulas at a meta-level we use thesymbols F, G and H.The transformation rules for quantified relational logic are:1. For any predicate symbol P and for any two place relationsymbol R, given any constants a or b or any variables x or y,Pa, Px, Rab, Rxy are formulas. In Px and Rxy formulas, x andy are said to "free" variables because there are no quantifiers towhich they are bound.2. If F is a formula by Rule 1 and if x is a free variable in F, then3x F is a formula and Vx F is a formula. Rule 2 is known asbinding any free variable x in F by a quantifier.A formula F formed by either rule 1 and 2 is called an atomicformula.3. If F and G are atomic formulas, then -F, (F v G), (F ^ G),· G) and (F ↔ G) are complex formulas.(F4. If H is a complex formula, then the result of binding any freevariable in H is a formula.

The picture showing the transformation rules of the quantified relational logic.The formulas…

Question 1 In this exercise use the transformation rules given in the picture uploaded, to verify that the following are formulas of quantified relational logic. (a) Ba (b) ¬Bb (c) ∃x¬Bx (d) ∃x(Rx ∧ ¬Bx) (e) ¬∀x(Rx → Bx) (f) ((Rb ∧ ¬Bb) → ∃x(Rx ∧ ¬Bx)) (The image shows rules and formulas if your not familiar with this)

Question 1 In this exercise use the transformation rules given in the picture uploaded, to verify that the following are formulas of quantified relational logic. (a) Ba (b) ¬Bb (c) ∃x¬Bx (d) ∃x(Rx ∧ ¬Bx) (e) ¬∀x(Rx → Bx) (f) ((Rb ∧ ¬Bb) → ∃x(Rx ∧ ¬Bx)) (The image shows rules and formulas if your not familiar with this)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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