course notes - Theory and Logic Group
... Proof. Suppose that such a Γ exists and let I Γ. We have M ( I iff M is finite. Consider ∆ t I u Y tLn | n ¥ 1u. Let ∆0 be a finite subset of ∆, then ∆0 t I u Y tLn | 1 ¤ n ¤ mu for some m and every structure of size m 1 is a model of ∆0 . So by the compactness theorem ∆ would have a model whi ...
... Proof. Suppose that such a Γ exists and let I Γ. We have M ( I iff M is finite. Consider ∆ t I u Y tLn | n ¥ 1u. Let ∆0 be a finite subset of ∆, then ∆0 t I u Y tLn | 1 ¤ n ¤ mu for some m and every structure of size m 1 is a model of ∆0 . So by the compactness theorem ∆ would have a model whi ...
Statistics Review Day 16: Counting, Probability, and Logic Problems
... Example 6: A four digit pin number is needed to access a bank account. How many different four-digit pin numbers are possible if no number can be used twice and the first and third digits must be odd, and the second and fourth numbers must be even? ...
... Example 6: A four digit pin number is needed to access a bank account. How many different four-digit pin numbers are possible if no number can be used twice and the first and third digits must be odd, and the second and fourth numbers must be even? ...