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Category > Programming Posted 28 Apr 2017 My Price 9.00

### CS 245 Assignment 3

Question 1,4,5 . Â Please answered Â in clearly handwriting and full steps

Â

Â

CS 245 Assignment 3
Due Date 5PM, Mon. March 6th. All questions are worth the same amount. Please ensure that your name and student number
appear, in ink, on each page of your assignment.
Work is to be done individually.
Assignment Questions
1. Let G be a set and Â· a binary operator on G. The pair &lt; G, Â· &gt; form a mathematical
group if
(i) for all f, g âˆˆ G, (f Â· g) is an element of G.
(ii) there is an element, e âˆˆ G, called the identity, such that for all g âˆˆ G: (e Â· g) = g
and (g Â· e) = g.
(iii) Â· is associative: that is for all f, g, h âˆˆ G: (f Â· (g Â· h)) = ((f Â· g) Â· h).
(iv) for each g âˆˆ G there is an inverse element g 0 âˆˆ G such that (g Â· g 0 ) = e and
(g 0 Â· g) = e.
Express the four group requirements (known as the axioms of group theory) in First
Order Logic. 2. Prove that ((Â¬âˆ€xA(x)) â†” âˆƒx(Â¬A(x))) is valid. 3. Show that âˆ€xâˆ€y(S(y) â†’ F (x)) |= âˆƒyS(y) â†’ âˆ€xF (x). 4. Show that âˆ€xâˆƒy(P (x) âˆ¨ Q(y)) |= âˆƒyâˆ€x(P (x) âˆ¨ Q(y)) 5. Either prove that
âˆ€x(P (x) â†’ Q(x)) |= âˆ€x(P (x) âˆ§ Q(x))
or show that the second formula is not a logical consequence of the second.

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# Answers (7)
Status NEW Posted 28 Apr 2017 03:04 AM My Price 9.00

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