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Consider the expression t ∈ instructor ∧ ∃ s ∈ department (t [dept_name] = s [dept_name]) the variables t and s are _____ respectively. 
  • a)
    Free variable and bound variable
  • b)
    Bound variable and free variable
  • c)
    Free variable and free variable
  • d)
    Bound variable and bound variable
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider the expression t ∈ instructor ∧ ∃s ∈ depa...
Concept:
In tuple relational calculus, there exists two quantifiers, namely universal quantifier and existential quantifier. For these, there are two types of variables: free variable and bound variable.
  • A tuple variable t is bound if it is quantified, meaning that it appears in existential or universal quantifier clause, otherwise it is free. Formally, tuple variable is free or bound as :
  • An occurrence of a tuple variable in a formula F that is an atom is free in F.
  • An occurrence of a tuple variable t is free or bound in a formula made up of logical connectives – (F1 AND F2), (F1 OR F2), NOT(F1) and NOT(F2)- depending on whether it is free or bound in F1 or F2. In a formula of the form F = (F1 AND F2) or F = (F1 OR F2), a tuple variable may be free in F1 and bound in F2 or vice versa.
  • All free occurrences of a tuple variable t in F are bound in F’ of form F’ = (∃ t) F or F’ = (for all t)F
Here, given expression is :
t ϵ instructor ∧ ∃ s ∈ department (t [dept_name] = s [dept_name])
According to above rules:
t is the free variable and s is the bound variable.
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Consider the expression t ∈ instructor ∧ ∃s ∈ department (t [dept_name] = s [dept_name]) the variables t and s are _____ respectively.a)Free variable and bound variableb)Bound variable and free variablec)Free variable and free variabled)Bound variable and bound variableCorrect answer is option 'A'. Can you explain this answer?
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