Problem set 6

Assigned: Mar. 25
Due: Apr. 1

Problem 1

Consider the first order language, with a domain of people and instants of time and the following non-logical symbols:
B(u,v) --- Time u is before time v.
D(p,t) --- Person p is dead at time t.
L(p,t) --- Person p is alive at time t.
R(p,q) --- Person p is a parent of person q.
U(p,t) --- Person p is not yet born at time t.
A -- Amy
N --- Now (a time).
Express the following sentences:

Problem 2

Let S be the sample space with 8 elements: S = { a,b,c,d,e,f,g,h }.
Let W be the event {a,b,c}; let X be the event {a,d,f,g}; let Y be the event {b,f,g} and let Z be the event {e,g}.
Let P(a)=0.2; P(b)=0.10; P(c)=0.10; P(d)=0.15; P(e)=0.14; P(f)=0.09; P(g)=0.06; P(h)=0.16.

A. Compute the values of P(W), P(X), P(Y), P(Z), P(W,X), P(Y,Z), P(X|W), P(W|X), P(Y|W), P(Z|W), P(Y|X), P(Z|X), P(Z|X,Y), P(Y,Z|X).

B. Are W and X absolutely independent? Are Y and Z absolutely independent? Are Y and Z conditionally independent given X?