Write in formal way of the following statements Is the argum

Write in formal way of the following statements. Is the argument valid or invalid? if the book is returned within 2 weeks, then there is no fine. you pay a fine or you may not check out another book. You are allowed to check out another book Therefore, the book was not returned within 2 weeks. Write the negation of each of the following two statement For all real numbers x and y with x

Solution

p - Book is returned within 2 weeks

q - fine is paid

r - check out for other books

a) p-->~q

b) q v ~r

c) r

d) ~p

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a) If the book is not returned within 2 weeks, there is fine.

b) You do not pay fine and check out for other book or you pay fine and do not check out for other book

c) You are not allowed to check for another book.

d) Therefore the book was returned within 2 weeks.