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Recent questions tagged discrete-mathematics

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Kenneth H. Rosen
Let P (x) be the statement “x can speak Russian” and let Q(x) be the statement “x knows the computer language C++.” Express each of these sentences in terms of P ...
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Kenneth H. Rosen
Related to inhabitants of an island on which there are three kinds of people: knights who always tellthe truth, knaves who always lie, and spies (called normals by Smully...
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Kenneth H. Rosen - Propositional Logic
Explain, without using a truth table, why (p ∨ ¬q) ∧ (q ∨ ¬r) ∧ (r ∨ ¬p) is true when p, q, and r have the same truth value and it is false otherwise.
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Kenneth H. Rosen - Propositional Logic
Which of these sentences are propositions? What are the truth values of those that are propositions?a) Boston is the capital of Massachusetts.b) Miami is the capital of F...
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Kenneth H. Rosen -- Equivalence Realtion Doubt
Find the smallest equivalence relation on the set {a, b, c, d, e} containing the relation {(a, b), (a, c), (d, e)}.
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Counting
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 least five femal...
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Function Composition Question Oscar Levin Qn. 20
Let $f : X \rightarrow Y$ and $g : Y \rightarrow Z$ be functions. We can define the composition of $f$ and $g$ to be the function $g \circ f : X \rightarrow Z$ for which ...
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ISI PCB 2023 Q1
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 always lies. A...
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Kenneth H. Rosen, Chapter 1
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 profe...
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Charles C Pinter Abstract Algebra
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.(Click on link..I have not shown th associa...
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Poset
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 greatest elementB. There exists ...
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self doubt
how to check the validity of an a argument using laws of logics
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Discrete Mathematics | Set Theory | Relation | Equivalance Relation
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 set defines a part...
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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 1
If $A$ and $B$ are two sets and $A \cup B = A \cap B$ then$A=\phi$$B=\phi$$A\neq B$$A=B$
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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 2
The cardinality of the power set of $A \cup B$, where $A=\{2,3,5,7\}$ and $B=\{2$, $5,8,9\}$, is?
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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 3
What is the Cartesian product of $A=\{1,2\}$ and $B=\{a, b\}$ ?$\{(1, a),(1, b),(2, a),(b, b)\}$$\{(1,1),(2,2),(a, a),(b, b)\}$$\{(1, a),(2, a),(1, b),(2, b)\}$$\{(1,1),(...
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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 4
Let $\mathcal{P}(A)$ denote the power set of $A$. If $\mathcal{P}(A) \subseteq B$ then$2^{|A|} \leq|B|$$2^{|A|} \geq|B|$$2|A|<|B|$$2^{|A|} \geq 2^{|B|}$
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GO Classes CS 2025 | Weekly Quiz 5 | Set Theory | Question: 5
Let $\mathrm{A}$ be a finite set of size $\mathrm{n}$. The number of elements in the power set of $A \times A$ is:$2^{n^2}$$\left(2^n\right)^2$$\left(2^2\right)^n$None of...
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