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Some examples from this set of practice questions
1.
What is the definition of the subset A ⊆ B?
Answer: The definition of the subset A ⊆ B is ∀x[ x ∈ A: x ∈ B] or t ∈ A (=val) t ∈ B.
2.
What is the definition of A = B?
Answer: The definition of A = B is ∀x[ x ∈ A <=> x ∈ B] or t ∈ A (|=val) t ∈ B or A ⊆ ^ B ⊆ A.
3.
What is the definition of t ∈ A^c?
Answer: The definition of t ∈ A^c? is ¬ ( t ∈ A).
4.
What is the definition of the powerset C ∈ P(A)?
Answer: The definition of the powerset C ∈ P(A) is C ⊆ A.
5.
What is the definition of an image?
Answer: The definition of an image is x ∈ A\' (|=val) F(x) ∈ F(A\') and also y ∈ F(A\') (|=val) ∃x[ x ∈ A\': F(x) = y].
6.
What is the definition of a source?
Answer: The definition of a source is x ∈ F^(<-) (B\') (=val) F(x) ∈ B\'.
7.
What is the definition of a surjection?
Answer: The definition of a surjection is ∀y[ y ∈ B: ∃x[ x ∈ A\': F(x) = y]].
8.
What is the definition of a bijection?
Answer: The definition of a bijection is ∀y[ y ∈ B: ∃^(1)x[ x ∈ A\': F(x) = y]] (which is the same as a surjection but with ∃^(1)).
9.
What is the definition of an injection?
Answer: The definition of an injection is ∀x1,x2[ x1, x2 ∈ A: (F(x1) = F(x2)) => (x1 = x2)].
10.
What is the definition of strong induction?
Answer: The definition of strong induction is as follows: ∀n[ n ∈ N: A(n)] {...} ∀k[ k ∈ N: ∀j[ j ∈ N ^ j < k: A(j)] => A(k)]
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