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A) (B D),C B,A D A C [ ](iv) (T S),(S (T U)) S (T U) [ ](v) C B,B D,(C D) A A [ ](vi) P Q,Q ... B, if A B then A (B).(iii) For any sets A and B, if A (B) then (A) (B).(iv) For any sets A,B and C,(A B)(B

a) Show each of the following [40]:. (i) P Q, Q R, P R P (ii) A B (B A) (A B) (iii) (A B) C, B C, (C A) (C ... i. x(Fx y(x = y Gy Rxy)), Fa, Fb, a = b xyz(x = y x = z y = z).

A C• A C• A C [ ]. (b) State and prove the Disjunctive Normal Form Theorem. [ ... You may rely upon your answer to part (b). [ ]. (d) Are the connectives ‘’, ‘’, ‘’ and ‘’ jointly expressively adequate?

2) Use truth-tables (complete or partial) to assess the following:(a) A B, B C, A B C(b) (A B) (A B)(c) (A B)(B A). ... SECTION BAnswer any two questions from section B.(6) Using the following symbolisation key:.

OR (b) Must an egalitarian be a democrat? 2. In what sense, if any, is democracy paradoxical? ... How should egalitarians deal with unequal natural endowments? 8. ‘If A rightfully interferes with B, B’s freedom is not thereby reduced.’ Discuss.

True. (A B) (B C) = {(x,y)|(x Ax B) (y B y C)}. ... Pr(B). (B) You are held captive in the Bayesian Republic of Zembla.

14 P TND, 4–5, 6–13. 1. (ii) A B (B A) (AB). ... 10]. AB = {(a, b)|a A b b} = {x|x = x}P(A) = {x|x A}A B (A B A = B).

iii) The set of ordered pairs, one of which is a labrador and the other of whichis a bulldog.L B B L. ... iv) The set of ordered pairs, one of which is a labrador other than Fido and theother of which is a bulldog.(L {f}) B B (L {f}).

12 b = a E, 11, 10. 13 Gb b = a I, 8–12. ... X) Pr(Y ). 11. Pr(A|B) = Pr(AB)Pr(B). (b) I draw three cards at random without replacement from a standard pack ofcards.

A B C A B B C A B CF T F T T T F. ... c) (A B)(B A)This claim is true, as the following complete truth table shows.