For each of the English statements below, do the following;
i. Define one or more propositional functions and rewrite the English statements using symbolic notation. Assume the universe of discourse is the set of positive integers.
ii. Is the statement true? Justify your answer.
iii. Write the negation of the symbolic notation, simplifying when possible.
iv. Rewrite the negation as an English statement.
v. Is the negated statement true? Justify your answer.
a) There exists an x and y such that x-y=y-x.
b) For every x and y,x-y=y-x.
c) For every x and y there exists a z such that (x)/(y)=z.
3. For each of the English statements below, do the following;
i.
Define one or more propositional functions and rewrite the English statements using symbolic notation. Assume the universe of discourse is the set of positive integers. Is the statement true? Justify your answer. Write the negation of the symbolic notation, simplifying when possible. Rewrite the negation as an English statement. Is the negated statement true? Justify your answer
ii. iii. iv. V.
a)There exists an x and y such that x-y = y-x. b)For every x and y, x-y = y-x. c) For every x and y there exists a z such that x/y = z.