G(x,y): x > y
I(x): x is an integer.
E(x): x is even.
N(x): x is a natural number.
(a) Not all numbers are even.
(b) 5 is not even.
(c) Not every integer is positive (i.e. greater than 0).
(d) A number is even only if it is integer.
(e) For an integer to be a natural number, it is necessary that it is nonnegative (i.e. not less than 0).
2. Fill in the blanks with the shortest string of characters so that the resultant proposition is valid.
(a)
(b)
(c)
(d)
(e)
. 3. Find the converse and the contrapositive of the following propositions:
(a) I can't complete the task, if I don't get more help.
(b) I will stay only if you go.
(c) Getting 95 in the final is sufficient for getting an A in Math 101.
(d) To get an A in Math 101, it is necessary for you to get an A in the final.
4(a) Express the argument given below using a symbol for each proposition.
(b) Using the symbols of (a) for the propositions, explain how the reasoning proceeds i.e. identify each application of modus ponens in the argument.
(c) Is the reasoning correct ? Give your reasons.