524 531. Given (1) All aB is c or D, (2) All BE is DF or cdF, (3) All C is aB or BE or D, (4) All bD is e or F, (5) All bf is a or C or DE, (6) All bcdE is Af or aF, (7) All A is B or CDEf or cDf or cdE ; shew that (i) All A is B, (ii) All C is D, (iii) All E is F. [K.]
532. Shew the equivalence between the two following sets of propositions:
| (1) | All A is BC or BE or CE or D ; |
| All B is ACDE or ACde or cdE ; | |
| All C is AB or AE or aD ; | |
| All D is ABCE or Ace or aC ; | |
| All E is AC or aCB or Bc. | |
| (2) | All a is BcdE or bcde or bD ; |
| All b is a or ce or dE ; | |
| All c is AbDe or abde or BdE ; | |
| All d is abce or BcE or Be or bE ; | |
| All e is ab or bc or d. |
533. Given
| (1) | All bc is DE or Df or hk, |
| (2) | All C is aB or DEFG or BFH, |
| (3) | All Bcd is eL or hk, |
| (4) | All Acf is d, |
| (5) | All k is BC or Cd or Cf or H, |
| (6) | All ABCDEFG is H or K, |
| (7) | All DEFGH is B, |
| (8) | All ABl is f or h, |
| (9) | All ADFKl is H, |
| (10) | All ADEFH is B or C or G or L ; |
shew that All A is L.[K.]
CHAPTER VI.
THE INVERSE PROBLEM.
534. Nature of the Inverse Problem.—By the inverse problem is here meant a certain problem so-called by Jevons. Its nature will be indicated by the following extracts, which are from the Principles of Science and the Studies in Deductive Logic respectively.