Summerizw the reasons for rejecting authority, induction, and experiment or experimentation as methods of proof in mathematics.
All x are y
All x are z
Some w are y
Which conclusions are correct:
(a) some z are y
(b) some y are x, but not x
(c) some x are not w
(d) some x are w
2006-11-28 01:19:57 · 6 answers · asked by magt_g 1 in Science & Mathematics ➔ Mathematics
Please I need the proof not the answer
2006-11-28 01:34:44 · update #1
Draw two circles one containing y and the other containing .z.
Let these two circles intersect each other and call the common area of intersection x. This satisfies conditions the all x are y and all x are z conditions
Now draw a third circle that contains w and let it intersect the circle containing all y. This satisfies the some w are y condition.
From this diagram, it is clear that conclusion (a) is correct. Those z that are also x are also y.
Conclusion (b) is not clear to me. If you mean some y are x but some y are not x, then this is true. Only those y that lie within the intersection of the y and z circles are also x. The rest of the y are not x.
(c) is not true under the conditions given. There is nothing to suggest that w circle should include x. The only condition is that some w include y. All x are not w would be true, but some x are not w implies that some x are w, which is not necessarily the case.
(d) Not true. Same argument as for (c). It is possible to draw circle w such that it includes part of circle y, part of circle z and part of their intersection x, but the conditions do not suggest this be done.
Hope this leads you to further thinking.
2006-11-28 02:30:41 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
This doesn't give a conclusive answer, and (b) looks wrong. the best way to answer this question is to draw a venn diagram, a) is true, b) is not clear, if the second x is W then it's true, c) possibly, but realisticly probably ALL x are not w, but you can't be sure, similarly it's not clear about d) without more information.
2006-11-28 01:33:04 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Since all x are y and all x are z, then y and z must overlap. Therefore (a) must be true. The rest are not.
2006-11-28 01:37:26 · answer #3 · answered by T 5 · 0⤊ 0⤋
from my point of view its A C D
2006-11-28 01:31:36 · answer #4 · answered by Danish 2 · 0⤊ 0⤋
c and d are correct
2006-11-28 01:29:08 · answer #5 · answered by James Chan 4 · 0⤊ 0⤋
c & d
2006-11-28 01:32:44 · answer #6 · answered by Theresa 2 · 0⤊ 0⤋