This is just a silly question.
2006-12-30 12:52:08 · 14 answers · asked by Link 5 in Science & Mathematics ➔ Other - Science
no, not necessarily, but they can.
draw a circle and call it trogs. then draw a smaller circle inside and call it grogs. (all grogs are trogs)
now draw another circle for clogs that only part of it overlaps the trog circle, some of the space is both clogs and trogs, but not touching the grog circle. then draw another circle for clogs that includes part of both the trog and grog circles.
So no, grogs and clogs are not necessarily the same, but they can be, depending if the clog and grog circles overlap inside the trog circle.
For really bad grog clogs, I recommend Brain-o. No lye.
2006-12-30 13:02:03 · answer #1 · answered by Squirrley Temple 7 · 3⤊ 2⤋
Nope, and the easiest way to see this is to draw a Venn diagram. These are circles which make logical relationships easier to understand in some cases than words:
Draw a big circle and label it Trogs.
Draw a smaller circle completely inside the big circle and label it Grogs.
Now for those versatile Clogs. "Some Trogs are Clogs" means that a circle representing Clogs could either overlap the Trog circle or be entirely inside it. This statement says nothing about the relationship of Clogs to Grogs, however. The Clog circle could overlap, be inside of, be completely around, or miss the Grog circle completely, so it is not logically necessary that "some Grogs are Clogs."
2006-12-31 00:16:37 · answer #2 · answered by hznfrst 6 · 1⤊ 1⤋
No it is not. Let us assume the following sets for Grogs, Trogs and Clogs:
Grogs: {1,2,3,4,5}
Trogs: {1,2,3,4,5,6,7,8,9,10}
Clogs: {7,8,9,10}
This fits the initial statement as all of the members of the Grogs set are members of the Trogs set and some of the members of the Trogs set are also members of the Clogs set. However, none of the members of the Grogs set occur in the Clogs set. Therefore, the initial statement has been met without an intersection of the Grog and Clog set, so it is not logically necessary that some Grogs are Clogs.
2006-12-30 21:02:56 · answer #3 · answered by Magic One 6 · 3⤊ 1⤋
No. Since only some Trogs are Clogs, it doesn't have to be the Trogs that are Grogs. It is possible that no Grogs are Clogs.
2006-12-31 00:53:17 · answer #4 · answered by I don't think so 5 · 0⤊ 0⤋
Ya. If all Grogs are Trogs then there are no Trogs, only Grogs.
So you're really asking 'Are some Grogs Clogs.' The answer is yes.
2006-12-30 21:49:01 · answer #5 · answered by Anonymous · 1⤊ 1⤋
No because you could have two categories of trogs. There could be the trog-clogs and the trog-grogs. It is not necessary for some grogs to be clogs.
2006-12-30 21:38:21 · answer #6 · answered by buffy132008 2 · 1⤊ 0⤋
yes transitive prop
G(grogs) = T (trogs)
T=C (clogs)
simplify it and take out the two T's
G = C
some grogs are clogs
2006-12-31 03:28:45 · answer #7 · answered by Anonymous · 0⤊ 1⤋
Not necessarily, no. All of the grogs-that-are-trogs may be among the trogs that are not clogs..
(All humans are mammals, and some mammals are beavers; but no humans are beavers. Well, not "officially" anyway)
2006-12-30 21:26:08 · answer #8 · answered by Tim P. 5 · 2⤊ 1⤋
Yes, by the Transitive Postulate of Logical Statements
2006-12-30 21:00:07 · answer #9 · answered by YOOOO 2 · 2⤊ 1⤋
Lots of frogs on logs, wear clogs, but dogs in bogs play pogs
2006-12-30 20:54:59 · answer #10 · answered by Big hands Big feet 7 · 1⤊ 3⤋