Given Two Relations R and S, Where R Contains N₁ $\cup$

Essay

Given two relations R and S, where R contains N₁ tuples and S contains N₂ tuples (N₂ > N₁ > 0), give the minimum and maximum cardinality for the result relation for each of the following relational algebra expressions and in each case state any assumptions about the schemas that are required to make the expression meaningful:
(a) R $\cup$ S
(b) R $\cap$ S
(c) R - S
(d) R x S
(e) $\sigma$ a = 1(R)
(f) $\Pi$ _a(R)