a) Translate the following sentence into a symbolic logic form. If John will work only if...

a) Translate the following sentence into a symbolic logic form.

If John will work only if he gets a raise, then we should get him a raise if we want the job done.

Use the following notations in your translation.

W: John works.

R: John does get a raise.

S: We should get John a raise.

D: We want the job done.

b) Give the contraposition of your answer in (a) . Try to simplify the logical form as much as possible. Show your work. Translate it back into English.

c)Show that the contraposition in (b) is logically equivalent to your answer in (a).

d)Translate the following sentence into a symbolic logic form. You are required to use quantifiers in your translation.

If there exists someone that will work if they don’t get a raise, then we don’t have to get everyone a raise to get the work done.

Use the following notations:

S: the set of workers

W(x): x works.

R(x): x gets a raise.

S(x): We have to get x a raise to get the work done.

Solutions

Expert Solution

NOTE: PLEASE UPVOTE IF FOUND HELPFUL

venereology answered 6 days ago

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