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

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.