Questions without a selected answer in Discrete Mathematics

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Suppose A, B, and C are subsets of a universal set U. Also suppose that n(U) = 150 n(A) = n(B) = 2n(C) = 50, $A\cap B\cap C = ∅$ ... . How many elements are in at least two of the sets A, B, and C?
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For any undirected connected graph \( G \), let \( \chi(G) \) be the minimum number of colours needed to colour all the vertices of \( G \) in such a way that no two adjacent ... i}, v_{i+1}\right) \) is an edge for \( 1 \leq i \leq k \)
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Suppose that there are nine students in a discrete mathematics class at a smallcollege.a) Show that the class must have at least five male students or at ... the class must have at least three male students or at least seven femalestudents.
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Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be functions. We can define the composition of $f$ and $g$ ... $f$ and $g$? Explain.
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Suppose there are three types of people in the world.A person is honest if the person always speaks the truth. A person is a liar if the person ... , deduce with appropriate justifications who among A, B and C has committed the crime.
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When three professors are seated in a restaurant, the hostess asks them: Does everyone want coffee? The first professor says: I do not know. The second ... to the professors who want it. How did she figure out who wanted coffee?
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Let DFA , M = (Q, ∑, δ, q$_0$, F) and Relation R is defined on Q as R:Q$\rightarrow$Q such that pRq iff $\forall$ w ∈ $\Sigma$* [ δ*(p,w) ∈ F ... δ* (q, w) ∉ F] then ____________ A) R is ReflexiveB) R is SymmetricC) R is transitiveD) None
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If G is a group, G=(F(R), +), F(R) set of all real valued functions.H={f€F(R) ; f(-x)=-f(x)}Is H a subgroup of G?My solution. ... addition is always associative) please let me know if iam correct.https://ibb.co/sPzHg6mhttps://ibb.co/sPzHg6m
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Consider the poset ({3,5,9,15,24,45},|). Which of the following is correct for the given poset? A. There exists a least element but not a ... element and a least elementD. There does not exist a greatest element and a least element
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Consider a matrix A (n×m) ,X(m×n) and B(n×n) such that AX=B . If A has k linearly independent columns then what conclusions can we nake about the number of linearly independent columns of B.
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Let $K_n$ denote the complete graph on $n$ vertices, with $n ≥ 3$, and let $u$, $v$, $w$ be three distinct vertices of $K_n$. Determine the number of distinct paths from $u$ to $v$ that do not contain the vertex $w$.
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how to check the validity of an a argument using laws of logics
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which if the following statement is True for every set?a. $\exists$ a equivalence class that is also a partition set.b. Every equivalence relation on a ... that is also equal to equivalence class of the set on some equivalence relation.
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If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then$A=\phi$B=\phi$A\neq B$A=B$
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The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?
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What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ?$\{(1, a),(1, b),(2, a),(b, b)\}$\{(1,1),(2,2),(a, a),(b, b)\}$\{(1, a),(2, a),(1, b),(2, b)\}$\{(1,1),(a, a),(2, a),(1, b)\}$
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Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is:$2^{n^2}$\left(2^n\right)^2$\left(2^2\right)^n$None of the above
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Which one of the following is/are true?$R \cap S=(R \cup S)-[(R-S) \cup(S-R)]$R \cup S=(R \cap S)-[(R-S) \cup(S-R)]$R \cap S=(R \cup S)-[(R-S) \cap(S-R)]$R \cap S=(R \cup S) \cup(R-S)$
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Let $A$ and $B$ be sets in a finite universal set $U$. Given the following : $|A-B|,|A \oplus B|,|A|+|B|$, and $|A \cup B|$ Which of the following is in order of increasing size ... |<|A-B|<|A \cup B|$|A-B|<|A \oplus B|<|A \cup B|<|A|+|B|$
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Let $A=\{0,1\} \times\{0,1\}$ and $B=\{a, b, c\}$. Suppose $A$ is listed in lexicographic order based on $0<1$ and $B$ is in alphabetic order. If $A \times B \times A$ is listed in ... )$((1,1), c,(0,0))$((1,1), a,(0,0))$((1,1), a,(1,1))$
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Which of the following statements is $\textbf{TRUE}$?For all sets $A, B$, and $C, A-(B-C)=(A-B)-C$.For all sets $A, B$, and $C,(A-B) \cap(C-B)=(A \cap C)-B$.For all ... $A, B$, and $C$, if $A \cap C=B \cap C$ then $A=B$.
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Which of the following statements is $\textbf{FALSE}$?$C-(B \cup A)=(C-B)-A$A-(C \cup B)=(A-B)-C$B-(A \cup C)=(B-C)-A$A-(B \cup C)=(B-C)-A$
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A non empty set A is termed as an algebraic structure ________a)with respect to binary operation *b)with respect to ternary operation ?c)with respect to binary operation +d)with respect to unary operation –
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The symmetric difference of sets $\text{A}=\{1,2, 3,4, 5, 6, 7, 8\}$ and $\text{B}= \{1, 3, 5, 6, 7,8,9\}$ is:$\{1, 3, 5, 6, 7,8\}$\{2, 4, 9\}$\{2, 4\}$\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$
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If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to$\{u,v,w,x\}$\{ x \}$\{u,v,w,x,y,z\}$\{u,v,w\}$
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