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!

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no. when the asker posts the question they can make a question worth what ever they think is a fair price. although it must be within the limit of the points they currently own. 5 is the minimum number of points a question can be worth. if a question is complicated or has lots of parts to it, it is better to make it worth more because more people will be more willing to answer.

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