Let R be the relation defined on the set of all processors by:
xRy iff x can carry out every instruction that y can carry out.
For example, every x86-compatible processor can carry out all the instructions of the original Intel 8086 processor. Thus, if x is such a processor, and y is the 8086 processor, then xRy.
As processor families evolved, more instructions were typically added to the original instruction set. For example, modern x86 compatible processors can carry out more instructions than the 8086.
There are examples of different processors that have the same instruction set. For example, the CMOS 6502 and 6510 processors have the same instruction set.
1. Check all properties that this relation has.
O Anti-symmetric
O Transitive
O Symmetric
O Reflexive

it is Anti-symmetric, transitive, reflexive but not symmetric

Step-by-step explanation:

hello,

By definition, a relation R on a set X is Anti-symmetric if for every a,b ∈ X, aRb and a≠b then bRa must not hold

or equivalently, if aRb and bRa, then a=b.

from the question, R is anti-symmetric because the more evolved processor can carry out all the instructions of the original processor but the converse may not hold since more instructions were added to the improved processor. that is, modern x86 can carry out all the instructions of 8086 but 8086 may not carry out all the instructions of x86, thus satisfying the first definition of Anti-symmetric property.

TRANSITIVE: R is also transitive beause by definition of transitivity, if aRb, bRc then aRc for all a,b,c ∈ x. thus if modern x86 carry out all the instructions of 8086 and 8086 carry out all the instructions of CMOS 6502, then definitely modern x86 must carry out all the instructions of CMOS 6502, hence satisfying transitive property.

SYMMETRIC: by definition, a relation R is symmetic if for all a,b ∈ X, aRb⇔ bRa. thus the processor is not symmetric since modern x86 carry out all the instructions of 8086 but 8086 may not carry out the instructions of modern x86.

REFLEXIVE: by definition, R is reflexive if for every a∈X, aRa, this means that a is related to itself, thus R is reflexive since every processor can carry out its instructions designed on it.

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.