Discrete Mathematics - It would be great if a full explanation would be provided. Thank you in advance.

2) 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," (Vx (I(x)=L(x)) "Dragonflies are insects," (Vx (D(x) >I(x))) "Spiders do not have six legs," (Vx (S(x)+-L(x))) "Spiders eat dragonflies." (Vx, y (S(x) AD(y)) E(x, y))) Identify the rule of inference that is used for the conditional statement "Vx, If x is an insect, then x has six legs" and the statement "Dragonflies are insects" to arrive at the conclusion "Dragonflies have six legs." A) modus ponens B) modus tollens C) hypothetical syllogism D) simplification