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

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

Database System Concepts
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
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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.
Transcribed Image Text: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.
Transcribed Image Text: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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