According to the definition, intervals like (a, b], [a, b) are half-open intervals. (3, 5] is the only one fits to this definition.  

• Every natural number is an integer. Every integer is a rational number. We do not consider the zero as a natural number.
• Every rational number has an infinite number of representations by fractions.
• Every rational number has a finite or infinite periodical representation.
• The term “number” means real number.
• There is one-to-one correspondence between the points of the real line and the set of real numbers.

As also understood from the information given, the correct answer is D. The statements regarding to the number sets and the real line in the options I “Every natural number is an integer. Every integer is a rational number.”, II “Every rational number has an infinite number of representations by fractions.” and IV “There is one-to-one correspondence between the points of the real line and the set of real numbers.”are correct. The statement in the option III “Every rational number has a finite periodical representation.” is not correct because of the fact that every rational number has a finite or infinite periodical representation.

log₂16=log₂2⁴=4

ln_e3=log_ee³=3 ,so

log₂16/ln_e3=4/3

Since x is both divisible by 2 and 3, it must be divisible to 6 for intersection. Then the intersection set contains 6, 12 and 18.

3^2z = 27 log₃ 27 = 81 ; z = 2 ; x = 100. Correct answer is E.

Now is the time to plot the graph of functions in order to make them visible to the eye. We will talk about the Cartesian coordinate system, a tool which enables us to view the graphs of functions.

Let us get acquainted with the Cartesian coordinate system. Two real lines intersecting perpendicularly at both their zeros constitute the Cartesian coordinate system. In this system, the horizontal real line is called the x-axis, or abscissa, and the vertical real line is called the y-axis, or ordinate. We call the point of intersection of the number lines as the origin.

As also understood from the information given, the correct answer is E. All of the statements regarding to graphs of functions in the options are correct.

x = A ∩ B ∩ C . pg. 10. Correct answer is C.

x^1/2 is not a natural number so x^1/2-3 is not a polynomial function. The answer is C.

x < 8. pg. 63. Correct answer is E.

The interval consisting of the elements of both intervals (-3, 7), and [4, 9) is [4, 7].

y = 2 . 2 + 3 = 7 ? 6. pg. 56. Correct answer is D.

The slope of y=5x+1 is 5 because the slope of a linear function of the form y=mx+n is m. The answer is B.

If all the sets under examination are subsets of some set U then U is called a universal set. Given two sets A and B:

• The set of all elements of the sets A and B is called the union of A and B
• The set of all elements both A and B is called the intersection of A and B
• The set of all elements of A which are not in B is called the difference of A and B
• The difference of U and A is called the complement of A.

As also understood from the information given, the correct answer is D. The statements in the options I “The set of all elements of the sets A and B is called the union of A and B “, II  “The set of all elements both A and B is called the intersection of A and B.”, and III “The set of all elements of A which are not in B is called the difference of A and B. are correct. The statement in the option IV “The difference of U and A is called the complement of U.” is not correct because of the fact that the difference of U and A is not called the complement of A not U.

The difference between the numerator and denominator is 1 in all given numbers. In this case the value of the ratio increases as the numerator (or denominator increases) For a simple example think of 1/2 and 2/3. 1/2=0.5 and 2/3=0.67. Thus the answer is E.

Extend the given fractions to the common denominator 10.

. The greatest fraction is 7/2. The answer is D.

change of base : x = (ln 9 / ln 2) (ln 8 / ln 5) (ln 25 / ln 9) = (1 / ln 2) (3 In 2 / In 5) (2 In 5) = 6. Correct answer is C.