Simplify the following statements. Which variables are free and which are bound? If the statement has no free variables, say whether it is true or false.
(a) w ∈ {x ∈ R | 13 − 2x > c}.
(b) 4 ∈ {x ∈ R | 13 − 2x ∈ {y | y is a prime number}}. (It might make this statement easier to read if we let P = {y | y is a prime number}; using this notation, we could rewrite the statement as 4 ∈ {x ∈ R | 13 − 2x ∈ P}.)
(c) 4 ∈ {x ∈{y | y is a prime number} |13 − 2x > 1}. , {y | y is a prime number} = P
Solutions:
(a) (w ∈ R) ∧ (13 − 2(4) > c) x us bound, c,w are free variablses
(b) (4 ∈ R) ∧ (13 − 2(4) ∈ P) bound variables x, y, no free variables TRUE
(4 ∈ R) ∧ (4 ¬∈ P) ∧ (13 − 2(4) > 1) bound variables x, y, no free varaibles FALSE
