Answer:
Step-by-step explanation:
Define Sets:
S(x): x was sick yesterday
W(x): x went to work yesterday
V(x): x was on vacation yesterday
Find:
Logical expression with the same meaning of:
(a) Everyone was well and went to work yesterday.
(b) Everyone who was sick yesterday did not go to work.
(c) Yesterday someone was sick and went to work.
(d) Someone who missed work was neither sick nor on vacation
(e) Ingrid was sick yesterday but she went to work anyway.
Solution:
a) Everyone was well and went to work. People who could have possibly gone to work would have been who were well or un-well so the the resulting set would be.
A (x) = W(x) - (W(x) & S(x))
b) Everyone who was sick and did not go to work. Sick people may or may not go to work. Hence, the domain can be defined as:
B (x) = S(x) - (W(x) & S(x))
c) Someone who was sick and did not go to work. Sick people may or may not go to work. Hence, the domain can be defined as:
C (x) ⊆ (W(x) & S(x))
d) Someone who missed work was not sick not on vacation:
D (x) = ( W'(x) & S'(x) & V'(x))
e) Ingrid was sick but went to work,, answer to part c and e are the same
E (x) = C(x) ⊆ (W(x) & S(x))
