Question on logic from the course "Introduction to mathematical thinking" on coursera

Question

The question goes this way:

Give a useful (and hence natural sounding) denial of each of the following statements.

Fred will go but he will not play.

This is how I attempted to solve the problem:

Let A: Fred will go and let B: He'll play. The statement says: (A(and)(not)B) So, the negation of this statement gives: ((not)A(OR)B)

So my answer is "Fred will not go or he'll play." but the answer key says : "Fred will not go but he'll play."

In my opinion "but" sound more like "and". So, how am I wrong?

(Please excuse my Mathjax skills)

In addition, we have to consider that the initial sentence is meaningful; thus also its negation must be. The proposed solution: "Fred will not go but he'll play" is meaningless: how can Fred play if he is not there ? — Mauro ALLEGRANZA, Jul 03 '20 at 11:46
Keeping the meaning of the sentence intact, my answer comes out to be - "Fred will play if he doesn't go." — professorchoki243, Jul 03 '20 at 15:54

Andreas Blass · Answer 1 · 2020-07-04T04:54:15.850

The answer key is simply wrong; "Fred will not go but he'll play" is not the negation of "Fred will go but he won't play." Your answer, "Fred will not go or he'll play" is logically correct, but one could argue whether it's "natural sounding". A logically equivalent but perhaps better-sounding formulation would be "If Fred goes then he'll play." (Remember that, in general, "(not A) or B" is equivalent to "A implies B.")

Question on logic from the course "Introduction to mathematical thinking" on coursera

1 Answers1