Define quantifier. Translate: For every person x, if x is a student in the class, then x has visited Dhaka and x has not visited USA.

Show that ∀x (P(x)^Q(x)) and ∀x P(x)^∀x Q(x) are logically equivalent.

Translate each of the following sentences into First Order Logic (FOL) i. Not all cars have carburetors. ii. All babies are illogical. iii. Every connected and circuit-free graph is a tree. iv. All that glitters is not gold.