Question 1

Let P be the relation defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party. Not being registered or being registered as an independent also counts as a registration.

Check all properties that P has.

Group of answer choices

reflexive

transitive

anti-symmetric

symmetric

Question 2

Let C be the relation defined on the set of all people by xCy if and only if x and y share a common interest (such as a hobby, a science, a sport, etc.) Consider that some people may have no interests at all.

Check all properties that C has.

Group of answer choices

reflexive

anti-symmetric

transitive

symmetric

Question 3

Let N be the "direct neighbor" relation defined on the set of all people: if x and y are persons, xNy iff x and y live directly next to each other, such as in two houses or apartments that are directly next to each other.

If there is at least one unit between them, then they don't live directly next to teach other.

Check all properties that this relation has.

Group of answer choices

Symmetric

Anti-symmetric

Reflexive

Transitive

Question 4

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.

Check all properties that this relation has.

Group of answer choices

Reflexive

Transitive

Symmetric

Anti-symmetric

Question 5

Let F be the relation on the set of commercial airports defined by:

If x and y are two such airports, xRy if there is a commercial flight that flies from A directly to B (non-stop).

Check all properties that the relation has and use common sense. In general when an airline offers a flight from A to B, there is always a return direct flight from B to A.

Group of answer choices

Transitive

Symmetric

Anti-symmetric

Reflexive