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Webpage for Mathematical Logic

Important Question Types:

  1. Checking validity of First Order Logic Statements
  2. Checking validity of Propositional Logic

Recent questions tagged mathematical-logic

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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 - 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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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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GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 5
Which of the following compound propositions is/are a tautology?$[p \land (p \rightarrow q)] \rightarrow q$$[q \land (p \rightarrow q)] \rightarrow p$$[(p \lor q) \land (...
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Does Either...Or means Exclusive Or or Inclusive Or?
Let's take a compound propositionsEither it is below freezing or it is snowing.Now if$p$: it is below freezing $q$: it is snowingWill it be $p \vee q$ or $p \oplus q$? Th...
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Why (p ∨ T) is not a tautology?
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GATE DS&AI 2024 | Question: 19
​​​​​​Let $x$ and $y$ be two propositions. Which of the following statements is a tautology /are tautologies?$(\neg x \wedge y) \Rightarrow(y \Rightarrow x)$$...
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GATE CSE 2024 | Set 2 | Question: 2
​​​​Let $p$ and $q$ be the following propositions:$p$ : Fail grade can be given.$q$ : Student scores more than $50 \%$ marks.Consider the statement: "Fail grade c...
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GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 58
Let $\mathrm{F}$ and $\mathrm{G}$ be two propositional formulae.Which of the following is/are True?If $F \vee G$ is a tautology then at least one of $F, G$ is a tautology...
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Memory Based GATE DA 2024 | Question: 33
Which of the following are tautologies? \(x \land \neg y \Rightarrow y \rightarrow x\)\(\neg x \land y \Rightarrow \neg x \rightarrow y\)\(x \land \neg y \Rightarrow \ne...
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Memory Based GATE DA 2024 | Question: 57
First-order logic question: All balls are round except rugby balls.
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GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 45
Below is a drawing(graph representation) of a binary relation $\text{R}$ over a set $\text{P}$ of elements $\{ \text{A, B, C, D, E, F}\}:$Which of the following first-ord...
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Mathematical Logic: Which of the following is a logical consequence of $∀x(p(x)∨q(x))$
The following question is on the NPTEL archive of Assignment 2 of Discrete Mathematics Course,(Link : assessment id-15 (nptel.ac.in)) . I am not able to get howthe answe...
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Computer Science - UGC NET 2021 [ Question ID = 2352 ]
Which of these statements about the floor and ceiling functions are correct ? Statement 1 : ⌊2x⌋ = ⌊x⌋ + ⌊x + (1/2)⌋ for all real numbers x.Statement 2 : ⌈x...
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Computer Science - UGC NET 2021 [ Question ID = 2351 ]
Which of the following are logically equivalent ?¬p - ( q - r ) and q - ( p v r )( p - q ) - r and p - ( q - r )( p - q ) - ( r - s ) and ( p - r) - ( q - s )Choose the ...
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# Discrete Mathematics
Simplify the above expression
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Mathematical Logic
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Mathematical Logic
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Mathematical Logic
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University of Illinois Chicago UIC Math 215 Fall 2010, Test 1 Propositional Logic
Consider the following statement:If I get a perfect score on this test, then I am a genius.Decide which of the following is logically equivalent to the statement above.a)...
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Permutations
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Doubt on First Order Logic
Can anyone explain this how this implication is valid with an example∃x (Px ⊕ Qx) < ∃xPx ⊕ ∃xQx
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How many n-digit sequences formed from the symbols 0, 1, 2, 3 and 4 contain at least one 0, at least one 1 and at least one 2? Solve by using the Inclusion/Exclusion Principle.
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#Discrete
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Engg Maths lec video 5a Go classes
Is pivot columns and basic variables same thing?? or basic variables are the first elements of non zero rows in echelon matrics??
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