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Consider the expression t ϵ instructor ∧ ∃ s ϵ 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?
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Most Upvoted Answer
Consider the expression t instructor ∧ ∃ s department (t [...
Explanation:
Free variable and bound variable:
- In the expression provided, variable t is a free variable as it is not bound by any quantifiers.
- Variable s is a bound variable as it is bound by the existential quantifier ∃.
Therefore, the variables t and s are respectively a free variable and a bound variable. This distinction is important in understanding the scope of variables and their relation to quantifiers in logical expressions.
Free variable and bound variable:
- In the expression provided, variable t is a free variable as it is not bound by any quantifiers.
- Variable s is a bound variable as it is bound by the existential quantifier ∃.
Therefore, the variables t and s are respectively a free variable and a bound variable. This distinction is important in understanding the scope of variables and their relation to quantifiers in logical expressions.
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Community Answer
Consider the expression t instructor ∧ ∃ s department (t [...
- 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 ϵ department (t [dept_name] = s [dept_name])
t ϵ instructor ∧ ∃ s ϵ department (t [dept_name] = s [dept_name])
According to above rules:
t is the free variable and s is the bound variable.
t is the free variable and s is the bound variable.
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