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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
