All instructed people know that Flaps, Fleps and Flips are simply forms of Flops.

It is proved moreover that all Fleps are both Flips and Flops.

However there is a complication: Recently one found out that there are some Flips which are neither Flaps nor Fleps nor Flups, and in addition one found out that there are some Fleps which are neither Flaps nor Flups.

Admittedly, some Flaps and some Fleps and some Flups are Flips.

And now we know more about Flups: Some are Fleps, some are Flips, and some are both Flaps and Fleps.

In this common universe:

a) Are there Flips which are Flups, which are not Flops?

b) If a Flap is a Flep, then is it always a Flip?

c) If a Flap is a Flep, some of them could it be a Flup?

d) There is a creature that is both a Flap and a Flep and a Flip and a Flop and a Flup?

There are SUM(FACT(5)/(FACT(k)*FACT(5-k)), for k = 1 to 5 combinations of Flaps, Fleps, Flips, Flops and Flups -- i.e., 31 combinations.

Excluding the combinations where Flaps, Fleps and Flips are not Flops, leaves 17 combinations. Further, excluding from the remaining combinations where Fleps are not both Flips or Flops leaves 13 combinations. And these are:

1. Flap  Flep  Flip  Flop  Flup
2. Flap  Flep  Flip  Flop     
3. Flap        Flip  Flop  Flup
4.       Flep  Flip  Flop  Flup
5. Flap        Flip  Flop     
6. Flap              Flop  Flup
7.       Flep  Flip  Flop     
8.             Flip  Flop  Flup
9. Flap              Flop  Flup
10.             Flip  Flop  Flup
11.                   Flop  Flup
12.                   Flop
13.                         Flup

Therefore,
a) No. There is only one possible combination (#13) in which exists a creature that is not a Flop. That creature could only be
a Flup.

b) Yes. There are only two possible combinations (#1 & #2) where a Flap is also a Flep. In both cases the creature is also a Flip.

c) Yes. Of the two possible combinations where a Flap is also a Flep, one of the combinations is where the creature is also a Flup (#1).

d) Yes. Only one combination (#1) exists where a Flup is both a Flap and a Flep. This combination also has the creature as a Flip and a Flop.

 

Edited on November 18, 2008, 4:48 am

Posted by Dej Mar on 2008-11-16 14:34:08