702 Appendix C • Answers & Hints for Selected Exercises- "'"' (P V "'"' Q) := "'"'P A "'"'"'"' Q := "'"'PA Q
- "'"' [(P V Q) => R] = (P V Q) A "'"'R
- "'"'[P => (Q => R)] :=PA"'"' (Q => R) :=PA (QA"'"' R)
- "'"'[(QA P) =>(RV SJ:= (QA P) A"'"' (RVS):= (QA P) A("'"' RA"'"' S)
- "'"' (JAM) = "'"' JV"'"' M. John is not innocent or Mary's charge is not a
lie. - "'"'(C => 0) =CA"'"' 0. You come tonight but I don't order pizza.
33."'"' (CV F) ="'"'CA"'"' F. I am not going to the concert and I am not going
to the football game.
- "'"'(T => P) =TA"'"' P. This statement is true but I can't prove it.
- "'"'("'-'PA"'"' C) =PVC. 1 is a prime number or 1 is a composite number.
- "'"'[H => (G VS)]= HA("'-' GA"'"' S). You come to my house tonight but
I don't grill a steak and I don't make stir fry.
EXERCISE SET A.2Part A:- 't/x, [L(x) => W(x)]; domain= {people}
- "'"':Jx 3 [A(x) A M(x)] or 't/x, ["'-' A(x) V"'"' M(x)] or 'tfx, [A(x) => "'"'M(x)];
domain = {people} - [:Jx 3 G(x)]A"'"' [:Jx 3 C(x)] or [:Jx 3 G(x)]A ['t/x,"'"' C(x)]; domain= {people
in this room} - :Jx 3 [L(x)A"'"' G(x)]; domain= {people}
- 't/x, [G(x) => C(x)]; domain= {people in this room}
- "'"':Jx 3 x^2 + 3x -1 = 0, or 't/x, x^2 + 3x - 1 # 0; domain= {real numbers}
- :Jx 3 ["'"' A(x)] or"'"' 't/x, A(x); domain= {your ideas}
- ['t/x, E(x)]A"'"' ['tfx, S(x)] or ['t/x, E(x)] A [:Jx 3 "'"'S(x)]; domain= {people}
- 't/x, [E(x) => :Jy 3 "'"'H(y)]; domain of x and y ={people}
- 't/x, 't/y, B(x, y), where B(x, y) = x is brother of y; domain of x and y =
{people} - "'"' :Jx, "'"' :Jy 3 [x # y A L(x, y)] or 't/x, 't/y, [x # y => "'"' L(x, y)], where
L( x, y) = x looks exactly like y; domain of x and y = {people}