Question

3. One of the set operators in the relational algebra can be expressed in terms of the other set operators. Which one is it? Give the algebraic expression in terms of the other set operators. (15 points) 4. Do the operations below commute ? Explain your answer. (7 points) $\Pi_{A_1, A_2}(\sigma_{A_1=x}(R)) = \sigma_{A_1=x}(\Pi_{A_1, A_2}(R))$ 5. Suppose you are given the relational schema R(A1, A2,..., An). Under what con- dition is the following equation true? (8 points) $|\Pi_{A_1}(R)| = |R|$ where $|A|$ stands for the cardinality of A. 6. Give an algebraic expression for the join operator in terms of the other algebra operators. (10 points)

          3. One of the set operators in the relational algebra can be expressed in terms of
the other set operators. Which one is it? Give the algebraic expression in terms
of the other set operators. (15 points)
4. Do the operations below commute ? Explain your answer. (7 points)
$\Pi_{A_1, A_2}(\sigma_{A_1=x}(R)) = \sigma_{A_1=x}(\Pi_{A_1, A_2}(R))$
5. Suppose you are given the relational schema R(A1, A2,..., An). Under what con-
dition is the following equation true? (8 points)
$|\Pi_{A_1}(R)| = |R|$ where $|A|$ stands for the cardinality of A.
6. Give an algebraic expression for the join operator in terms of the other algebra
operators. (10 points)

3. One of the set operators in the relational algebra can be expressed in terms of
the other set operators. Which one is it? Give the algebraic expression in terms
of the other set operators. (15 points)
4. Do the operations below commute ? Explain your answer. (7 points)
ΠA1, A2(σA1=x(R)) = σA1=x(ΠA1, A2(R))
5. Suppose you are given the relational schema R(A1, A2,..., An). Under what con-
dition is the following equation true? (8 points)
|ΠA1(R)| = |R| where |A| stands for the cardinality of A.
6. Give an algebraic expression for the join operator in terms of the other algebra
operators. (10 points)

Added by Ruben J.

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