\"A predicate is said to be \"autopredicable\" if the result of applying it to i

Question

"A predicate is said to be "autopredicable" if the result of applying it to itself is a true statement. For example, the predicate P(x) = "x appears on MAT 311 Homework #10" is autopredicable, because the statement " "x appears on MAT 311 Homework #10" appears on MAT 311 Homework #10" is a true statement. Another example of an autopredicable statements would be Q(x)="x is written with fewer than 500 letters."

a) Is the predicate "x is heteroprediable" heteropredicable?

b) Is the predicate "x is autoprediable" autopredicable?

Explanation / Answer

Part a

Yes. Because the statement "x is heteropredicable" is not autopredicable and thus is heteropredicable. (Autopredicable and Heteropredicable are disjoint sets).

Part b

Yes, The predicate "x is autopredicable" is autopredicable,because the statement "x is autopredicable" is autopredicable is a true statement.

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