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Prolog Programming Language :
Probably programming languages are procedural: than the programmer specifies exactly the right instructions (algorithms) required to get an agent to function correct. Well it comes as a surprise to many people in which there is another way to write programs. Declarative programming is whenever the user declares what the output to a function should look such given some information about the input. So after that the agent searches for an answer that fits the declaration, so that returns any it finds.
According to given an example, just visualize a parent asking their child to run to the shop and buy some groceries. Now for do this in a declarative fashion, there the parent simply has to write down a shopping list first. So the parents have "programmed" their child to perform their particular task in the knowledge in which the child has underlying search routines that will enable him or her to catch to the shop, and come home after find and buy the groceries.
Just to instruct their child in a procedural fashion, and they would have to tell the child to go out of the front door, and then turn left, and walk down the street, than stop after 70 steps, so on.
Simplified the Boolean Algebra (x + y)(x + z) simplifies to ? Ans. x + yz as simplified the Boolean Algebra expression. [(x + y) (x + z)] = xx + xz + xy + yz = x + xz + xy + y
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