Final answer:
The question asks if a value y can exist such that for all z, w(y, z) is equivalent to w(David Belcher, z) even if y is not equal to David Belcher. To answer this, one must understand the properties of the function w, as the possibility of such a y existing depends on whether w gives unique outputs for unique inputs.
Step-by-step explanation:
The student's question seems to concern the concept of function and equivalence in mathematics. It is attempting to determine if there is a value y such that y is not equivalent to a particular value (David Belcher in this case), and yet, when a function w is applied to both y and z, the outcome is the same as applying w to 'David Belcher' and z. The question uses a logical structure common in college-level mathematics, especially within the fields of abstract algebra or formal logic.
To address this question, one would need to know more about the properties of the function w. If w is such that it produces unique outputs for unique input pairs, then the statement w(y, z) = w(David Belcher, z) for all z implies that y must indeed be equivalent to 'David Belcher'. However, if multiple inputs can produce the same output in function w, it is possible for y to be different from 'David Belcher' and still satisfy w(y, z) = w(David Belcher, z) for all z.