If we let the domain be all animals, and S(x) = "x is a spider", I(x) = " x is an insect", D(x) = "x is a dragonfly", L(x) = "x has six legs", E(x, y ) = "x eats y", then the premises be

"All insects have six legs," (∀x (I(x)→ L(x)))
"Dragonflies are insects," (∀x (D(x)→I(x)))
"Spiders do not have six legs," (∀x (S(x)→¬L(x)))
"Spiders eat dragonflies." (∀x, y (S(x) ∧ D(y)) → E(x, y)))
The conditional statement "∀x, If x is an insect, then x has six legs" is derived from the statement "All insects have six legs" using .

a. existential generalization
b. existential instantiation
c. universal instantiation
d. universal generalization

The conditional statement "∀x, If x is an insect, then x has six legs" is derived from the statement "All insects have six legs" using "a. existential" generalization

Step-by-step explanation:

In predicate logic, existential generalization is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier in formal proofs.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.