All Questions
Tagged with discrete-mathematics first-order-logic
774
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Is the law of non-contradiction part of formal mathematics?
I am seeking hereby to clarify whether the law of non-contradiction is part of the framework in which mathematicians work or not. Wikipedia says only that this is a principle in "logic", ...
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1
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Confusion on Question from Kenneth Discrete Math Textbook
Suppose there are signs on the doors to two rooms. The sign on the
first door reads “In this room there is a lady, and in the other one
there is a tiger”; and the sign on the second door reads “In one ...
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Prove whether two formulas are logically equivalent to each other
Going through the exercises in my textbook, I have been given formulas
$F = \exists x(B(x) \wedge C(y))$ and $G = \exists y(B(y) \wedge C(y))$ and asked to prove whether (1): $F \Rightarrow G$ and/or (...
- 79
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Null Quantification Rosen's Discrete Math Textbook Exercise Confusion/Clarification
From Discrete Math Rosen textbook 8th edition Section 1.4 Exercises:
Exercise 48-51 establish rules for null quantification that we can
use when a quantified variable does not appear in part of a ...
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1
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101
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Do these two logic transaltions have the same meaning?
From Rosen's Discrete Math textbook:
Translate the statement “Every real number except zero has a
multiplicative inverse.” (A multiplicative inverse of a real number $x$
is a real number $y$ such ...
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1
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48
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Clarification on logical equivalence [duplicate]
So is this correct to say that 2 + 2 = 4 ≡ 3 + 2 = 5, since both are true statements? It's a simple question but usually when logical equivalence is mentioned it's mostly seen between two propositions ...
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1
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1
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Trying to understand logical equivalence and discourse domain
From Rosen's Discrete Math textbook, where they define logical equivalence involving quantifiers:
"Statements involving predicates and quantifiers are logically
equivalent if and only if they ...
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1
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31
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Quantifiers with restricted domain
Screenshot from Discrete Math Rosen Textbook.
Note that the restriction of a universal quantification is the same as the universal quantification of a conditional statement. For instance, ∀x < 0 ($...
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Clarification on "domain of discourse" for a quantified propositional formula in context of logical equivalence. [duplicate]
Screenshots from Rosen's discrete Math textbook.
Here's how they define logical equivalence involving quantifiers:
Statements involving predicates and quantifiers are logically equivalent if and only ...
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2
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54
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Can you provide me an example of quantifiers with their scopes overlapping?
Screenshot comes from Rosen's Discrete Math Textbook.
Scope (as per textbook): The part of a logical expression to which a quantifier is applied is called the scope of this quantifier.
The textbook ...
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Free Variables in Quantified Proposition (from Discrete Math Rosen Textbook)
I'm just confused 2 things:
Based on what I underlined in red, would the statement (also underlined in red) "there exists an x such that x + y = 1" (I'll assume domain of discourse for x ...
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4
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Confusion on using "unless" more than once in proposition
I'm having trouble interpreting this highlighted sentence (from Discrete Math Rosen Textbook) properly due to using unless more than once in this sentence. I understand that q unless (not p) is the ...
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1
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67
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Really lost on how propositions Q4 and Q5 were derived: n-Queen problem Discrete Math Rosen Textbook
The context is the well-known n-Queens problem and on the textbook, the following compound proposition is given:
Let $p(i,j)$ be a proposition that is $True$ iff there's a queen in the $i$th row and $...
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1
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Confusion on Section 1.2 of Rosen's Discrete Math Textbook
So I was able to deduce based on the rule that p implies q is the same as q unless (not p) that this is same as:
(not s) -> (r -> (not q))
I could use the logical equivalence (A -> B) = (A or ...
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-3
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1
answer
76
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The $n$th statement in a list of $100$ statements is "Exactly $n$ of the statements in this list are false". What can we conclude? [closed]
The $n$th statement in a list of $100$ statements is "Exactly $n$ of the statements in this list are false".
For this problem, based on the screenshotted answer, would the part I highlighted ...
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