## Question

###### Semantics of First Order LogicConsider the universe U consisting of all finite lists of natural numbers, and a binary relation P that we interpret as the prefix-of relation, that is P(T,y) holds if â‚¬ is a prefix of y. For example_ we have that â‚¬ is a prefix of the list [1,2,3] and only if x â‚¬ {[L, [1], [1,2], [1,2,3]}. Formally; we are considering situation (U, 0) where U is the set of finite lists of natural numbers and O(P) {(I,y) prefix of y}: For each of the follwing formulae, determin

Semantics of First Order Logic Consider the universe U consisting of all finite lists of natural numbers, and a binary relation P that we interpret as the prefix-of relation, that is P(T,y) holds if â‚¬ is a prefix of y. For example_ we have that â‚¬ is a prefix of the list [1,2,3] and only if x â‚¬ {[L, [1], [1,2], [1,2,3]}. Formally; we are considering situation (U, 0) where U is the set of finite lists of natural numbers and O(P) {(I,y) prefix of y}: For each of the follwing formulae, determine all situations (U, 0) where U is aS above, and 0( P) is the pretix relation, in which the respective formula is true, and justify your answer in a single sentence Vz Jygz(P(y;x) ^ P(z,1)) 4. Vy(Vz(P(T, 2) + P(z,y)) VzVy(P(z, y) V P(y; 1)) 5. Vx(P(T,y) - P(c,2)) VzVy(P(z,y) ~ P(z,2)) Vy( (Vz(P(E, 2)) - P(z;y))