11 Maths – 1 – Sets – Complete Chapter – Test 1 (FREE MCQ Test)
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Which of the following is an infinite set?
A set which is not finite (does not have a definite number of elements) is infinite, such as the set of natural numbers.
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For any set \( A \), the double complement \( ( A’ )’ \) is equal to:
The law of double complementation states that \( ( A’ )’ = A \).
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The value of \( A \cap A’ \) for any set \( A \) is:
By the complement laws, the intersection of a set and its complement is always the empty set \( \phi \).
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What is the roster form of the solution set of the equation \( x^{2} + x – 2 = 0 \)?
Solving \( x^{2} + x – 2 = 0 \) gives \( ( x – 1 ) ( x + 2 ) = 0 \), so \( x = 1, -2 \).
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Which Greek symbol is used to denote the phrase ‘belongs to’?
The Greek symbol \( \in \) (epsilon) is used to denote that an element belongs to a set.
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What is the complement of the universal set, \( U’ \)?
By the laws of the empty set and universal set, \( U’ = \phi \).
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If \( U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } \) and \( A = { 1, 3, 5, 7, 9 } \), what is \( A’ \)?
The complement \( A’ \) contains all elements of the universal set U that are not in A.
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According to De Morgan’s Law, \( ( A \cup B )’ \) is equal to:
De Morgan’s Law states that the complement of the union of two sets is the intersection of their complements.
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The set of letters forming the word ‘SCHOOL’ is represented in roster form as:
In roster form, elements are not generally repeated. Thus, ‘SCHOOL’ becomes \( { S, C, H, O, L } \).
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In set-builder form notation, what does the colon symbol \( : \) stand for?
In the description of a set, the braces stand for “the set of all” and the colon stands for “such that”.
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If \( A = { a, b, c, d } \) and \( B = { d, c, b, a } \), then \( A \) and \( B \) are:
Two sets are equal if they have exactly the same elements, regardless of the order of listing.
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How is the set \( A = { 1, 4, 9, 16, 25, \dots } \) represented in set-builder form?
The elements are squares of natural numbers, represented as \( { x : x = n^{2}, \text{ where } n \in N } \).
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Who is considered the primary developer of the modern theory of sets?
German mathematician Georg Cantor (1845-1918) developed the theory of sets.
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Two sets \( A \) and \( B \) are called disjoint if:
Disjoint sets are sets that have no common elements, meaning \( A \cap B = \phi \).
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If \( V = { a, e, i, o, u } \) and \( B = { a, i, k, u } \), find \( V – B \).
The difference \( V – B \) is the set of elements which belong to V but not to B.
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If \( A = { 2, 4, 6, 8 } \) and \( B = { 6, 8, 10, 12 } \), find \( A \cup B \).
The union \( A \cup B \) consists of all elements of A and B, taking common elements only once.
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What is a set with only one element called?
A set that contains only a single element is referred to as a singleton set.
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A set \( A \) is said to be a subset of a set \( B \) if:
A is a subset of B if every element of A is also an element of B.
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How is the set \( { x : x \in R, -4 \leq x \leq 6 } \) represented in interval notation?
An interval excluding the lower bound and including the upper bound is written as \( ( a, b ] \).
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Which of the following is a well-defined collection of objects, thus forming a set?
A set is defined as a well-defined collection of objects where one can definitely decide if an object belongs to it.
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The set of real numbers \( { x : a \leq x \leq b } \) is called a:
A closed interval contains the end points and is denoted by \( [ a, b ] \).
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Which of the following is an example of the empty set?
An empty set contains no elements. There is no natural number between 1 and 2.
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If \( A \subset B \), then what is the value of \( A \cup B \)?
If B is a subset of A, then \( A \cup B = A \). Conversely, if \( A \subset B \), their union is the larger set B.
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If \( A = { 1, 2, 3 } \), what is \( A \cup \phi \)?
The empty set \( \phi \) is the identity element for the union operation; thus \( A \cup \phi = A \).
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If \( A \subset B \) and \( A \neq B \), then \( A \) is called a:
If A is a subset of B but not equal to B, it is specifically called a proper subset of B.
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