Let ????(?, ?, ?) be a predicate that
represents the statement “? makes a fool of ? on day ?.” Thus, for
example, ∃?: ∀?: ????(?, ???, ?) means that there is someone who
fools Lem every day.
Homework Answers
SOLUTION:
Given meaning with examples:
????(?, ?, ?) = “? makes a fool of ? on day ?.”
∃?: ∀?: ????(?, ???, ?) = "There is someone who fools Lem every day."
Answer:
- ∀x: ∀y: ????(Sam, x, y) VS ∀y:∀x: ????(Sam, x, y)
∀x: ∀y: ????(Sam, x, y) = “Sam makes a fool of everyone every day”
∀y:∀x: ????(Sam, x, y) = “Sam makes a fool of everyone every day”
No difference is the two statements
- ∃x: ∃y: ????(Sam, x, y) VS ∃y: ∃x: ????(Sam, x, y)
∃x: ∃y: ????(Sam, x, y) = “Sam fools some x on some days”
∃y: ∃x: ????(Sam, x, y) = “Sam fools some x on some days”
No difference is the two statements
- ∃x: ∀y: ????(Sam, x, y) VS ∀x: ∃y: ????(Sam, x, y)
∃x: ∀y: ????(Sam, x, y) = “There is someone whom Sam fools every day”
∀x: ∃y: ????(Sam, x, y) = “There are some days when Sam fools everyone”
The two statements are different as they give different meanings.
- ∃x: ∀y: ????(Sam, x, y) VS ∀y: ∃x: ????(Sam, x, y)
∃x: ∀y: ????(Sam, x, y) = “There is someone whom Sam fools every day”
∀y: ∃x: ????(Sam, x, y) = “There is someone whom Sam fools every day”
No difference is the two statements
- ∃x: ∀y: ????(Sam, x, y) VS ∃y:∀x: ????(Sam, x, y)
∃x: ∀y: ????(Sam, x, y) = “There is someone whom Sam fools every day”
∃y:∀x: ????(Sam, x, y) = “There are some days when Sam fools everyone”
The two statements are different as they give different meanings.
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