Let p(x) be some property that an input x may or may not have.
(a) explain how the following sentence says ‘there is exactly one x with the property p(x):
∃x(p(x) ∧ ∀y(p(y) → y = x))
(b) write similar sentences using quantifiers for
i. there are exactly two things with the property represented by p.
ii. there are at least two things with the property represented by p.
iii. there is at most one thing with the property represented by p.
note: the shorthand ∃! p(x) is a common shorthand for ‘there is exactly one x with the property p(x). do not use this shorthand in your solutions above!

If you embed a word table into powerpoint, what happens when you make edits to the embedded data? a. edits made to embedded data change the data in the source file; however, edits made to the source file will not be reflected in the embedded data. b. edits made to embedded data will change the data in the source file, and edits made to the source file will be reflected in the embedded data. c. edits made to embedded data don't change the data in the source file, nor will edits made to the source file be reflected in the embedded data. d. edits made to embedded data don't change the data in the source file; however, edits made to the source file will be reflected in the embedded data.