Solution Found!
Solved: Suppose the domain of the propositional function
Chapter 6, Problem 30E(choose chapter or problem)
Suppose the domain of the propositional functionP \((x, y)\) consists of pairs \(x\) and \(y\), where \(x\) is 1 , 2 , or 3 and \(y\) is 1,2 , or 3 . Write out these propositions using disjunctions and conjunctions.
a) \(\exists x P(x, 3)\)
b) \(\forall y P(1, y)\)
c) \(\exists y \neg P(2, y)\)
d) \(\forall x \neg P(x, 2)\)
Equation Transcription:
Text Transcription:
(x,y)
\exists x P(x, 3)
\forall y P(1, y)
\exists y \neg P(2, y)
\forall x \neg P(x, 2)
Questions & Answers
QUESTION:
Suppose the domain of the propositional functionP \((x, y)\) consists of pairs \(x\) and \(y\), where \(x\) is 1 , 2 , or 3 and \(y\) is 1,2 , or 3 . Write out these propositions using disjunctions and conjunctions.
a) \(\exists x P(x, 3)\)
b) \(\forall y P(1, y)\)
c) \(\exists y \neg P(2, y)\)
d) \(\forall x \neg P(x, 2)\)
Equation Transcription:
Text Transcription:
(x,y)
\exists x P(x, 3)
\forall y P(1, y)
\exists y \neg P(2, y)
\forall x \neg P(x, 2)
ANSWER:Solution:
Step1
Given that
Let us assume that the domain of the propositional function P(x, y) consists of pairs x and y, where x is 1, 2, or 3 and y is 1, 2, or 3.
Step2
To find
Write out these propositions using disjunctions and conjunctions.
Step3
We have to know about
Disjunctions:-It is a compound statement that can be formed by joining two statement by OR operator.Symbol “”.
Conjunctions:-It is a compound statement that can be formed by joining two statement by AND operator.Symbol “”.
Step4
We have
The domain of the propositional function P(x, y) consists of pairs x and y, where x is 1, 2, or 3 and y