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Recent questions tagged goclasses2024-dm-2-weekly-quiz
3
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 1
Consider a Set $\text{X} = \{a, b, c, d, e\}$ and a relation $\text{R}$ defined on $\text{X}:$ $\text{R} = \{(a, a), (a, b), (a, e), (b, b), (b, e), (c, c), (c, d), (d, d), (e, e)\}.$ Which of the following properties is Not true for $\text{R}?$ reflexive symmetric anti-symmetric transitive
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 5
Let $\text{N}$ be the set of positive integers. Consider the relation $\text{R}$ on $\text{N}$ defined by $x\text{R}y$ if and only if $\gcd(x,y)>1.$ The relation $\text{R}$ on $\text{N}$ is ________ Reflexive Symmetric Transitive Equivalence relation
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3
GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 7
A relation $\text{R}$ on a set $\text{A}$ is said to be triangular iff $a\text{R}b$ and $c\text{R}b$ together imply $a\text{R}c,$ For all $a,b,c \in \text{A} \,\,\,and \,\,\, a \neq c.$ ... $\text{S}$ is a transitive relation. If a relation $\text{S}$ is transitive and triangular, then $\text{S}$ is a symmetric relation.
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 9
We define a relation $\text{S}$ on a non-empty Set $\text{A}.$ The definition of relation $\text{S}$ ... $\text{A}$ on which such relation $\text{S}$ can be defined.
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 11
Let $\text{A, B}$ be two non-empty sets such that $\text{P(A)} \subset \text{P(B)},$ where $\text{P(S)}$ denotes Power set of set $\text{S}$, and $\subset$ denotes proper subset . Let $\text{M}$ be the universal set and ... $\{\text{A} \cap \text{B},\text{A}' \cap \text{B}'\}$
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 13
The below function is defined from a set of all positive integers to a set of all integers. ... statements is true? It is one to one but not onto It is onto but not one-one It is bijection It is neither One-One nor Onto
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 16
Let $\text{Z}$ be the set of all integers. Define a relation $\text{S}$ on $\text{Z} \times \text{Z}$ by $(w,x)\text{S}(y,z)$ if and only if $w-x = y-z.$ We know that $\text{S}$ is an equivalence relation. Which of the ... class of $(a,b)$ is disjoint from the equivalence class of $(a-2,b+2),$ for all $a,b,c,d \in \text{Z}.$
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 18
Let $\text{R}$ and $\text{S}$ be binary relations on a set $\text{A}.$ Suppose that $\text{R}$ is reflexive, symmetric, and transitive and that $\text{S}$ is symmetric, and transitive but is not reflexive ... and symmetric but not reflexive $\text{R} \cup \text{S}$ is reflexive and symmetric but may not be transitive.
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 21
Let $\text{A}$ be any set. The following are the definitions of Irreflexive and Asymmetric Relations : A binary relation $\text{R}$ on a set $\text{A}$ ... total order relation. Every strict order is antisymmetric. Every relation which is both Irreflexive and Asymmetric is in strict order.
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 22
Let $\text{Z}$ be the set of all integers. Which of these functions from $\text{Z}$ to $\text{Z}$ is not Onto $f(n) = n-1$ $f(n) = n^{2} + 1$ $f(n) = n^{3}$ $f(n) = \left \lfloor \frac{n}{2} \right \rfloor$
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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 23
Which of the following statements must be true? $\left \lfloor x \right \rfloor = \left \lceil x \right \rceil$ if and only if $x$ is an integer. $\left \lfloor x \right \rfloor + 1 = \left \lceil x \right \rceil$ if and only ... for all $x,y.$ $-\left \lfloor x \right \rfloor = \left \lceil -x \right \rceil $ for all $x.$
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