Answer
a) 0
b) 1
c) 0
d) 1
e) 0
f) 1
g) 0
Work Step by Step
Our domain is all integers.
a) $Q(0)$ is the probability that $0+1>2(0)$, so $Q(0)=0$
b) $Q(−1)$ is the probability that $−1+1>2(−1)$, so $Q(−1)=1$
c) $Q(1)$ is the probability that $1+1>2(1)$, so $Q(1)=0$
d) $∃xQ(x)$ is satisfied by $x=−1$, so $∃xQ(x)=1$
e) $∀xQ(x)$ is contradicted by $Q(0)$, so $∀xQ(x)=0$
f) $∃x¬Q(x)$ is satisfied by $Q(1)$, so $∃x¬Q(x)=1$
g) $∀x¬Q(x)$ is contradicted by $Q(−1)$, so $∀x¬Q=0$
