1. Determine whether the proposed negation is correct. If it is not, write a correct negation.
   statement: For all integers n, if n² is even then n is even.
   proposed negation: For all integers n, n² is even and n is not even.
   correct negation: There exist an integer n such that n² is even and n is odd
   
2. Given the argument:
   If something is intelligible then it never puzzles me.
   Logic puzzles me.
   \ Logic is unintelligible
   Circle the letter of any true statements regarding this argument:
   a. The argument is valid, Universal Modus Ponens.
   b. The argument is valid, Universal Modus Tollens. [correct answer]
   c. The argument is invalid, converse error.
   d. The argument is invalid, inverse error.
   e. The argument is valid, but not for the above reasons.
   f. The argument is invalid, but not for the above reasons.
   
   
   
   
3. Let our universe of discourse be the set of all functions U(x), P(x) = “polynomial functions”, D(x) = “differentiable functions”, and C(x) = “continuous functions”.
   Rewrite the following argument symbolically and determine its validity:
   
   For all functions, being a polynomial function is a sufficient condition for the function to be differentiable.
   
   Differentiable is a necessary condition for being continuous.
   
   \ All polynomial functions are continuous.

" x Î U(x), P(x) ® D(x)

~D(x) ® ~C(x)

\ P(x) ® C(x)