In accordance with rules already laid down, we have immediately—
Ace is BDF ;
Acf is BDE ;
ABcD is E or F.
463. Find the obverse of each of the following propositions:—
(1) Nothing is A, B, or C ;
(2) All A is Bc or bD ;
(3) No Ab is CDEf or Cd or cDf or cdE ;
(4) No A is BCD or Bcd ;
(5) Some A is not either bcd or Cd or cD. [K.]
497 464. Shew that the two following propositions are equivalent to each other:—No A is B or CD or CE or EF ; All A is bCde or bcEf or bce. [K.]
465. Contraposit the proposition, All A that is neither B nor C is both X and Y. [L.]
466. Find the full contrapositive of each of the following propositions:
(1) Whatever is B or CD or CE is A ;
(2) Whatever is either B or C and at the same time either D or E is A ;
(3) Whatever is A or BC and at the same time either D or EF is X ;
(4) All A is either BC or BD. [De Morgan.]
467. Find the full contrapositive of each of the following propositions:—
All A is BCDe or bcDe ;
Some AB is not either CD or cDE or de ;
Whatever is AB or bC is aCd or Acd ;
Where A is present along with either B or C, D is present and C absent or D and E are both absent ;
Some ABC or abc is not either DEF or def. [K.]
468. What information can you obtain about Af, Be, c, D, from the proposition All AB is CD or EF? [M.]
469. Establish the following: Where B is absent, either A and C are both present or A and D are both absent; therefore, where C is absent, either B is present or D is absent. [K.]