Question

Following set is given:

X := {Horse, Dog} 
Y := {Cat}

I define the set:

M := Pow(X) u {Y}

u for union

The resulting set of the power set operation is:

Px := {0, {Horse}, {Dog}, {Horse, Dog}}

0 for empty set

My question is referenced to the unio operation. How do I unite 0 and Y?

M := {{Horse, Cat}, {Dog, Cat}, {Horse, Dog, Cat}}

Answer 1

you have

M := Pow(X) u {Y}

with

Pow(X) := {0, {Horse}, {Dog}, {Horse, Dog}}

so

M := {0, {Horse}, {Dog}, {Horse, Dog}} u {{Cat}}

Does that clear it up for you?

The set you’ve displayed the union mapped over the cartesian product and missing {Cat}.