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Questions and Answers
Which of the following relations is reflexive, symmetric, and transitive?
Which of the following relations is reflexive, symmetric, and transitive?
- Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer} (correct)
- Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}
- Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}
- Relation R in the set A = {1, 2, 3,..., 13, 14} defined as R = {(x, y) : 3x – y = 0}
Which of the following relations is neither reflexive, symmetric, nor transitive?
Which of the following relations is neither reflexive, symmetric, nor transitive?
- Relation R in R defined by R = {(a, b) : a ≤ b3}
- Relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}
- Relation R in R defined as R = {(a, b) : a ≤ b}
- Relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2} (correct)
Which of the following relations is reflexive and transitive, but not symmetric?
Which of the following relations is reflexive and transitive, but not symmetric?
- Relation R in the set N of natural numbers defined as R = {(x, y) : y = x + 5 and x < 4}
- Relation R in the set A = {1, 2, 3,..., 13, 14} defined as R = {(x, y) : 3x – y = 0}
- Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}
- Relation R in R defined as R = {(a, b) : a ≤ b} (correct)
Which of the following relations is symmetric but neither reflexive nor transitive?
Which of the following relations is symmetric but neither reflexive nor transitive?
Which of the following relations is reflexive, but neither symmetric nor transitive?
Which of the following relations is reflexive, but neither symmetric nor transitive?
What type of relation is the relation R in the set R of real numbers defined by R = {(a, b) : a ≤ b3}?
What type of relation is the relation R in the set R of real numbers defined by R = {(a, b) : a ≤ b3}?
Which of the following functions is bijective?
Which of the following functions is bijective?
For the function f: R → R given by f(x) = [x], where [x] denotes the greatest integer less than or equal to x, which of the following properties is true?
For the function f: R → R given by f(x) = [x], where [x] denotes the greatest integer less than or equal to x, which of the following properties is true?
For the Modulus Function f: R → R given by f(x) = |x|, where |x| is x if x is positive or 0, and -x if x is negative, which of the following statements is correct?
For the Modulus Function f: R → R given by f(x) = |x|, where |x| is x if x is positive or 0, and -x if x is negative, which of the following statements is correct?
For the Signum Function f: R → R given by f(x) = 1 if x > 0, f(x) = 0 if x = 0, and f(x) = -1 if x < 0, which of the following properties holds?
For the Signum Function f: R → R given by f(x) = 1 if x > 0, f(x) = 0 if x = 0, and f(x) = -1 if x < 0, which of the following properties holds?
Let A = {1, 2, 3}, B = {4, 5, 6, 7}, and f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Which of the following properties does f possess?
Let A = {1, 2, 3}, B = {4, 5, 6, 7}, and f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Which of the following properties does f possess?
Consider the function f: R → R defined by f(x) = 3 - 4x. Which of the following properties does f possess?
Consider the function f: R → R defined by f(x) = 3 - 4x. Which of the following properties does f possess?
Which of the following best describes an equivalence relation?
Which of the following best describes an equivalence relation?
In the context of the given relation R, why are all elements of the subset {1, 3, 5, 7} related to each other?
In the context of the given relation R, why are all elements of the subset {1, 3, 5, 7} related to each other?
Why can no element from the subset {1, 3, 5, 7} be related to any element from the subset {2, 4, 6}?
Why can no element from the subset {1, 3, 5, 7} be related to any element from the subset {2, 4, 6}?
If a relation is reflexive, it means that:
If a relation is reflexive, it means that:
Symmetry in an equivalence relation implies that:
Symmetry in an equivalence relation implies that:
Transitivity in an equivalence relation means that:
Transitivity in an equivalence relation means that:
