1. 1 point each) Consider the statement: if x >2 , then x² > 4

a. Write the Contraposition of this statement.

b. Write the Converse of this statement.

c. Write the Inverse of this statement.

d. Write the Negation of this statement.

e. Is " x > 2 " a sufficient condition for " x² > 4 ?

f. Is " x > 2 " a necessary condition for " x² > 4?

1. (1 point each) For all integer k, m and n , if k is a factor of m . n , then k is a factor m or k is a factor of n.

a. Express this statement in a formal version using

b. Write the Contraposition of this statement.

c. Write the Converse of this statement.

d. Write the Inverse of this statement.

e. Write the Negation of this statement.

f. Prove this statement is false by providing a counter example.?

g. (2 points) Is the statement "For all integer k and m , if k is a factor of m² , then k is a factor m ." True or false ? Why?

h. (2 points) Is the statement "There exist integers k and m , such that k is a factor of m² and k is a factor m".

1. If an infinite series converse then its terms go to 0

a. (1 point) Write the Contraposition of this statement.

b. (1 point) Write the Converse of this statement.

c. (1 point) Write the Inverse of this statement.

d. (1 point) Write the Negation of this statement.

e. (3 points) What is the error in this argument:

1. Consider that statements:

a. such that x² -2xy + y² = 0

b. such that x² - 2 xy +y² = 0

which, if any, statement is true ? why ?