Discrete Math Chapter One Practice Questions

A universal statement assets that a certain property is ____ for ____.

true; all elements in a defined set

A conditional statement asserts that if one thing ____ then some other thing ____.

is true;, must also be true.

Given a property that may or may not be true, an existential statement asserts that _____ for which the property is true.

there exists at least one element

(Fill in the blanks using a variable or variables to rewrite the given statement)

Is there a real number whose square is -1?

a. Is there a real number x such that _____?

b. Does there exist ____ such that x^2 = -1 ?

a. x^2= -1

b. an element x in the set of R

(Fill in the blanks using a variable or variables to rewrite the given statement)

Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 4 when it is divided by 6?

a. Is there an integer n such that n has ____?

b. Does there exist ____ such that when n is divided by 5 the remainder is 2 and if _____?

Note: There are integers with this property, can you think of one?

a. a remainder of 2 when n/5 and a remainder of 4 when n/6.

b. an integer n; n is divided by 6 the reminder is 4

(Fill in the blanks using a variable or variables to rewrite the given statement)

Given any two real numbers, there is a real number in between.

a. Given any two real numbers a and b, there is a real number c such that c is _____.

b. For any two ____ , ____ such that a < c < b .

a. a < c < b

b. a and b in the set of R; there exists a c

(Fill in the blanks using a variable or variables to rewrite the given statement)

Given any real number, there is a real number that is greater.

a. Given any real number r, there is _____ such that ____.

b. For any ____ , _____ such that s > r.

a. a real number s, s > r

b. r in the set of R, there exists an s in R