##### Question 1: 1D Element: Domain Consistency

Assume an Element constraint for \(T[y]=z\), with:

- \(D(y) = \{0,1,2,3,4\}\)
- \(T = [5,5,5,10,8]\)
- \(D(z) = \{5,10\}\)

What is the domain of \(y\) after a domain-consistent filtering?

{0,1,2,3,4}

{0,1,2,3}

##### Question 2: 2D Element: Domain Consistency

Assume an Element constraint for \(T[x][y]=z\), with:

- \(D(x) = \{0,1,2\}\)
- \(D(y) = \{3\}\)
- \(T = [[1,8,9,6],[1,9,2,4],[9,8,9,8],[1,9,2,5]]\)
- \(D(z) = \{2,...,6\}\)

What is the domain of \(z\) after a domain-consistent filtering?

{6}

{5,6}

{4,6}

{2,...,6}

##### Question 3: 1D Element: Domain Consistency

Assume an Element constraint for \(T[y]=z\), with:

- \(D(y) = \{0,1,2,3,4\}\)
- \(T = [5,5,5,10,8]\)
- \(D(z) = \{5,6,7,8,9,10\}\)

What is the domain of \(z\) after a domain-consistent filtering?

{5,6,7,8,9,10}

{5,8,10}

{5,10}

##### Question 4: Stable Matching: Modeling

In the stable matching problem, the constraint "the company of the student of company c is c" is modeled with:

an Element constraint for \(T[x]=z\) where \(T\) is a 1D array of integer values, while \(x\) and \(z\) are variables.

an Element constraint for \(T[x,y]=z\) where \(T\) is a 2D array of variables, while \(x\), \(y\), and \(z\) are also variables.

an Element constraint for \(T[x]=z\) where \(T\) is a 1D array of variables, while \(x\) and \(z\) are variables.

an Element constraint for \(T[x,y]=z\) where \(T\) is a 2D array of integer values, while \(x\), \(y\), and \(z\) are variables.