## Chapter 14: PREDICATE LOGIC - Practice, Part B -

Multiple Choice:
Click on the button next to the answer you wish to select. Your results will be displayed immediately in the question's text box.

No. of Questions = 18

This is an exercise in recognizing instances of the inference and equivalence rules of predicate logic. You will be given an inference, and must indicate the name of the rule, using the standard abbreviations:

Quantifier-negation: QN
Universal instantiation: UI
Universal generalization: UG
Existential instantiation: EI
Existential generalization: EG

The following symbols have been used:

A tilde (~)indicates negation.
A lower-case "v" (v) indicates "or."
A greater-than symbol (>)indicates "if-then."
An asterisk (*) indicates "and."
An equals sign (=) indicates "if and only if."
An upper-case "E" (E) indicates the existential qualifier.

This exercise has two levels of difficulty: (a) questions 1-11 and (b) questions 12-18.

 1. (x)PxPa a) QN b) UI c) UG d) EI e) EG 2. (Ex)(Lx v Mx) Lg v Mg a) QN b) UI c) UG d) EI e) EG 3. Ga > Ha (x)(Gx > Hx) a) QN b) UI c) UG d) EI e) EG 4. Fb v Gb (Ex)(Fx v Gx) a) QN b) UI c) UG d) EI e) EG 5. (x)~(Px > Qx) ~(Pc > Qc) a) QN b) UI c) UG d) EI e) EG 6. (Ex)Mx Mb a) QN b) UI c) UG d) EI e) EG 7. (Ex)~(Px * Qx) ~(x)(Px * Qx) a) QN b) UI c) UG d) EI e) EG 8. (Ex)~Mx ~Mb a) QN b) UI c) UG d) EI e) EG 9. (x)Rax Rab a) QN b) UI c) UG d) EI e) EG 10. (x)(Mx > Nx) ~(Ex)~(Mx > Nx) a) QN b) UI c) UG d) EI e) EG 11. (Ex)[(Bx * Hdx) v Dx] (Ba * Hda) v Da a) QN b) UI c) UG d) EI e) EG 12. (Ex)[Px * (Sx > Tx)] Pc * (Sc > Tc) a) QN b) UI c) UG d) EI e) EG 13. (x)(y)[(Ax * By) > Fxy] (y)[(Am * By) > Fmy] a) QN b) UI c) UG d) EI e) EG 14. Pa > (y)(Sy > Ray) (x)[Px > (y)(Sy > Rxy)] a) QN b) UI c) UG d) EI e) EG 15. (x)(Ey)~[Bx > (Dxy v Fxy)] (x)~(y)[Bx > (Dxy v Fxy)] a) QN b) UI c) UG d) EI e) EG 16. (Pa * Qb) > (Sd > Tabd) (Ex)[(Pa * Qx) > (Sd > Taxd)] a) QN b) UI c) UG d) EI e) EG 17. (x)[Lg > (Mx * Pxg)] (Ey)(x)[Ly > (Mx * Pxy)] a) QN b) UI c) UG d) EI e) EG 18. (Pab * Sa) > (Ex)[(Rb * Qax) v Tbc] (y){(Pay * Sa) > (Ex)[(Ry * Qax) v Tyc]} a) QN b) UI c) UG d) EI e) EG

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