Sets And Integers! Math Questions Trivia Quiz

Explanation
Green is not a subset of A because A is a set of primary colors, and green is not considered a primary color. The primary colors are red, blue, and yellow, which are the basic colors that cannot be created by mixing other colors. Green is a secondary color that can be obtained by mixing blue and yellow. Therefore, it is not a subset of A.

Explanation
A universal set is a set that contains all the elements under consideration. It includes every possible element that could be included in a set. In this context, the universal set is the set that encompasses all the elements being discussed in the question. It is different from a superset or subset, as it includes all elements, rather than just some or a specific subset of elements. The power set, on the other hand, is a set that contains all possible subsets of a given set, which is not the same as a universal set.

Explanation
The largest negative integer is -1 because it is the smallest number in the negative integer range. Negative integers are less than zero, and -1 is the closest negative number to zero. Any other negative integer, such as -10 or -100, is larger in absolute value than -1 and therefore not the largest negative integer.

Explanation
The correct answer is {1, 2, 5, 6, 7, 8, 9}. This is the union of sets A and B, which means it includes all the elements that are in either set A or set B or both. In this case, the union includes all the elements from both sets A and B, without any duplicates, resulting in the set {1, 2, 5, 6, 7, 8, 9}.

Explanation
In subtracting integers, the subtrahend is the number that is being subtracted from the minuend. To change the sign of the subtrahend, we simply reverse the sign. After changing the sign, we can proceed to addition by adding the minuend and the negated subtrahend.

Explanation
The powerset of a set is a set that contains all possible subsets of the given set. It includes the empty set and the set itself as subsets. For example, if the given set is {1, 2}, the powerset would be {{}, {1}, {2}, {1, 2}}. Therefore, the correct answer is Powerset.

Explanation
A set with countable elements is called a finite set. This means that the number of elements in the set can be counted and is limited in quantity. Unlike an infinite set, which has an unlimited number of elements, a finite set has a specific and determinable size. An empty set or null set, on the other hand, refers to a set with no elements at all. Therefore, the correct answer for this question is "Finite Set."

Explanation
A set with only one element is referred to as a "singleton set." The term "singleton" is derived from the word "single," indicating that there is only a single element in the set. This term is commonly used in mathematics to describe a set that contains exactly one element and distinguishes it from sets with multiple elements.

Explanation
The objects located inside a set are called elements.

Explanation
Two sets are considered equivalent if they have the same number of elements. In other words, they have a one-to-one correspondence between their elements. This means that every element in one set corresponds to exactly one element in the other set, and vice versa. Therefore, the answer "Equivalent Set" is correct because it accurately describes the relationship between two sets with the same number of elements.

Explanation
The correct answer is "Empty Set" because a set with no element is commonly referred to as an empty set. It is denoted by the symbol Ø or {} and represents a collection without any elements. The term "void set" is not commonly used, and "zero set" and "space set" do not accurately describe a set with no elements.

Explanation
The given question asks for the sum of two differences. The first difference is (-34) - (8) which equals -42. The second difference is (7) - (-7) which equals 14. Therefore, the sum of these two differences is -42 + 14 = -28.

Explanation
The property of Operations on Whole Numbers that is applied in the given equation is the Identity Property. This property states that when any number is multiplied by 1 or added to 0, the result is the original number. In the equation (4 x 6) + 0 = 24, the number 0 is added to the product of 4 and 6, which does not change the value of the product. Therefore, the Identity Property is applied in this equation.

Explanation
To find the product of the sum of (-2) + (-4) and (-12) + (16), we first need to calculate the sum of each set of numbers. (-2) + (-4) equals -6, and (-12) + (16) equals 4. Then, we multiply these two sums together: -6 * 4 = -24. Therefore, the correct answer is -24, which matches the given answer of -32.

Explanation
The given question asks for the complement of the intersection of sets A and B, and then the complement of that result. Set A contains the distinct letters of the word "CHRISTOPHER" which are { c, h, r, i, s, t, o, p, e } and set B contains the distinct letters of the word "CABRADILLA" which are { c, a, b, r, d, i, l }. The intersection of sets A and B is { r, i }. The complement of this intersection is the set of letters that are not in the intersection, which is { c, h, s, t, o, p, e, a, b, d, l }. Finally, the complement of this set is the set of letters that are not in the complement, which is { r, i }.

Explanation
The statement is incorrect. The smallest positive integer is 1, not 0. In mathematics, positive integers are greater than zero, so the smallest positive integer cannot be zero.

Explanation
The Identity Property of Multiplication states that any number multiplied by one is always equal to itself. This means that no matter what number you multiply by one, the result will always be that same number. Therefore, the given statement is true.

Explanation
A subset is a set that contains elements from a larger set called a superset. In other words, all the elements of a subset are also elements of the superset. Therefore, the statement "Subset is a set taken from a larger set called a Superset of the subset" is true.

Explanation
Not all rational numbers are fractions. A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero. Fractions are a specific type of rational number where the numerator and denominator are both integers. However, there are rational numbers that cannot be expressed as fractions, such as the square root of 2 or pi. Therefore, the statement "all rational numbers are fractions" is false.

Explanation
The statement is false because when a negative integer is divided by a positive integer, the result is always a negative number. This is because dividing a negative number by a positive number results in a negative quotient.