Set Theory, Logic, and Proofs Flashcards

Weeks 1, 2 and 3 from Seq/series

1
Q

Given sets A and B, how do you show A=B?

A

A ⊂ B and B ⊂ A

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2
Q

What does A⊂B mean?

A

x∈A ⇒ x∈B

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3
Q

What is the converse of P⇒Q?

A

Q⇒P

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4
Q

What is the contrapositive of P⇒Q?

A

¬Q⇒¬P

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5
Q

Define “injective.”

A

f(x)=f(y) ⇒ x=y

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6
Q

Define “surjective.”

A

∀y∈B ∃x∈A : f(x)=y

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