Laws of logic: Could you make sure this question is proven correctly using the laws. laws of logic to show that ((s VrV¬r) ^ (¬s V¬rVq) ^ (rV¬s Vq)) = q v¬s. Step 1The commutative law deals with the order of operations or the sequence in which elements arearranged in an operation. In simple terms, the commutative law states that changing the order ofoperands in an operation does not affect the result.For example, the commutative law of addition states that for any two numbers a and b, a+b=b+a.This means that adding a and b gives the same result as adding b to a.Similarly, the commutative law of multiplication states that for any two numbers a and b, a*b-b*a.This means that multiplying a by b gives the same result as multiplying b by a.The commutative law is not limited to addition and multiplication operations but also to otheroperations. However, it is important to note that the commutative law does not apply to alloperations. For instance, the order of elements in a subtraction or division operation affects theresult, and hence, they are not commutative operations.Step 2((svr ((s vrv¬r) ^ (svrvq) ^ (rv¬svq)) = q v¬svs)^(vqv¬s) ^ (rv¬s vq)(rv¬rvs) ^ (qv¬sv¬r)^(rv¬svq)(rv¬svq) ^ (rvrvs) ^ (qv¬sv¬r)(Commutative law)(qv¬s) ^ (rv¬r Vs)(qv¬s) As(Given) (r V-r(Commutative law)(Commutative law)(simplification)(Elimination)(Addition)qv¬sThe solution is to use commutative law to rearrange the variables in the expression to make iteasier to apply other laws. Then it uses simplification and elimination to simplify the expression byremoving unnecessary variables. Finally, it uses the addition law to combine two variables into one.This proves the statement that the two expressions are equivalent.

Solution to the given question, Introduction: Commutative law: A.B=B.A A+B=B+A

Answered: ws of logic to show that ((s VrV¬r) ^…

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ws of logic to show that ((s VrV¬r) ^ (¬s V¬rVq) ^ (rV¬s Vq)) = q v¬s.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Laws of logic: Could you make sure this question is proven correctly using the laws.

laws of logic to show that ((s VrV¬r) ^ (¬s V¬rVq) ^ (rV¬s Vq)) = q v¬s.

Step 1
The commutative law deals with the order of operations or the sequence in which elements are
arranged in an operation. In simple terms, the commutative law states that changing the order of
operands in an operation does not affect the result.
For example, the commutative law of addition states that for any two numbers a and b, a+b=b+a.
This means that adding a and b gives the same result as adding b to a.
Similarly, the commutative law of multiplication states that for any two numbers a and b, a*b-b*a.
This means that multiplying a by b gives the same result as multiplying b by a.
The commutative law is not limited to addition and multiplication operations but also to other
operations. However, it is important to note that the commutative law does not apply to all
operations. For instance, the order of elements in a subtraction or division operation affects the
result, and hence, they are not commutative operations.
Step 2
((svr ((s vrv¬r) ^ (svrvq) ^ (rv¬svq)) = q v¬s
vs)^(vqv¬s) ^ (rv¬s vq)
(rv¬rvs) ^ (qv¬sv¬r)^(rv¬svq)
(rv¬svq) ^ (rvrvs) ^ (qv¬sv¬r)
(Commutative law)
(qv¬s) ^ (rv¬r Vs)
(qv¬s) As
(Given) (r V-r
(Commutative law)
(Commutative law)
(simplification)
(Elimination)
(Addition)
qv¬s
The solution is to use commutative law to rearrange the variables in the expression to make it
easier to apply other laws. Then it uses simplification and elimination to simplify the expression by
removing unnecessary variables. Finally, it uses the addition law to combine two variables into one.
This proves the statement that the two expressions are equivalent.

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