512. Eliminate R from the propositions All R is P or pq, All q is Pr or R, All qR is P. [K.]
513. Shew the equivalence between the following sets of propositions:—(1) a is BC ; b is AC ; C is Ab or aB ; (2) a is BC ; B is Ac or aC ; c is AB ; (3) A is Bc or bC ; b is AC ; c is AB. [K.]
514. Say by inspection, stating your reasons, which of the following propositions give information concerning A, aB, b, bCd, respectively: All Ab is bCd or c ; All bd is A or bC or abc ; Whatever is a or B is c or D ; Whatever is Ab or bc is bD or cD or e ; Everything is A or ab or Bc or Cd. [K.]
515. Determine the conditions under which a particular proposition affords information in regard to any given term. [K.]
516. It is known of certain things that the quality A is always accompanied by C and D, but never by B ; and further, that the qualities C and D never occur together, except in conjunction with A. What can we infer about C? [M.]
522 517. Given that everything that is Q but not S is either both P and or neither P nor R and that neither R nor S is both P and Q, shew that no P is Q. [K.]
518. Where C is present, A, B, and D are all present; where D is present, A, B, and C are either all three present or all three absent. Shew that when either A or B is present, C and D are either both present or both absent. How much of the given information is superfluous so far as the desired conclusion is concerned? [K.]
519. Given (i) All Pqr is ST ; (ii) Q and R are always present or absent together ; (iii) All QRS is PT or pt ; (iv) All QRs is Pt ; (v) All pqrS is T ; then it follows that (1) All Pq is rST ; (2) All Ps is QRt ; (3) All pQ is RSt ; (4) All pT is qr ; (5) All Qs is PRt ; (6) All QT is PRS ; (7) All qS is rT ; (8) All qs is pr ; (9) All qt is prs ; (10) All sT is pqr. [K.]
520. What can be determined about P in terms of Q and R from the premisses All P is Q or X, Some P is not RX? [K.]
521. Given that all honest men are happy, and that all dishonest men are unwise; and assuming that honest and dishonest, happy and unhappy, wise and unwise, are pairs of logical contradictories; what is all that can be inferred about men who are happy, unhappy, wise, unwise, respectively? [K.]