# Tagged Questions

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### Why relations are definied as the smallest

Often relations are definied as follows: The xxxxx relation is the smallest relation satisfying... My question is why relations are defined as the smallest ...
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### Let Alphabet have only one unary function of symbol f. Prove that every term must have 3K+1 symbols for some k≥0.

I believe in order to solve this question, I have to perform induction on the complexity of terms. But I'm not sure how to begin.
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### How to prove this logical equivalence using different laws?

Prove that $﹁p → (q→r)$ and $q → (p∨r)$ are logically equivalent using different laws. this is my answer: $﹁p → (q→r) = q → (p∨r)$ $(q→r) = ﹁q∨r$ implication equivalence $﹁p → (q→r) = p∨(﹁q∨r)$ ...
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### Alternate translation for: “Every real number except zero has a multiplicative inverse.”

A given text states, “Every real number except zero has a multiplicative inverse" (where mul- tiplicative inverse of a real number x is a real number y such that xy = 1). It offers the following ...
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### About $\Sigma=\{p_2\to p_1, p_3\to p_2,\, \dots\,\}$ . . .

Suppose $$\Sigma=\{p_2\to p_1, p_3\to p_2,\, \dots\,\}.$$ Which of the following is true? Explain your answer. For any $n$, $$\Sigma\cup\{p_n, \neg p_{n+1}\}$$ is complete and ...
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### Quick Truth Table in Logic Problem

Suppose We Have: How can quickly detect how many "1" are in the truth table of above formula? (without drawing Truth Table). i think by using some inference. any idea? we know there are 11 "1"s ...
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### prenex equivalence problem

Suppose: $$\forall x\exists y \phi(x,y) \to \neg \exists x\psi(x)$$ which of the following formula are prenex normal equivalence with the above formula? i didn't any idea to explain it. it's a ...
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### Either or in compound statement

I think this might be a silly question, but I'm confused. Please help me to understand it. Statement is: Randy studies German on either Tuesday or Friday. How should I write this as compound ...
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### Computable Set & Function

we know that i read this sentence are true? can anyone say an example for following sentence? there are a non computable set A such that
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### First Order Logic Consistency Big Problem

as i read some tutorial material on First Order Logic, i deduce that the following formula was consistent in FOL except the third one. am i right? i have doubt about the first one. any idea? thanks to ...
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### TAUTOLOGIES NP-Complete Condition

The decision problem TAUTOLOGIES is, Given $\forall x_1 \forall x_2 ... \forall x_n$ $\phi(x_1, x_2, ... x_n)$ a set of universally quantified Boolean variables and a Boolean formula ...
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### prenex normal equivalence challenges in math

consider these two following formula are prenex normal equivalence with the above formula? i think yes, but didn't have any idea to explain it.