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## [Part4] Element Constraint

##### 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?

##### 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?

##### 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?

##### 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: