# Set Theory - Question 1

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What happens if two columns are equal?
The relation is true.
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What does ~P mean?
Not P.
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Never true.
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What does tautology mean?
Always true.
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What does P => Q mean?
If P then Q.
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What is the truth table of P => Q?
Always true, apart from P=T and Q=F.
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What is P necessary for Q, in symbols?
Q => P.
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What is P sufficient for Q, in symbols?
P => Q.
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Draw the OR gate.
Triangle, from two lines to one.
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Draw the AND gate.
Curve, from two lines to one.
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Draw the NOT gate.
Triangle, one line throughout.
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What is Zorn's Lemma?
Let X be a non-empty partially ordered set in which every totally ordered subset has an upper bound. Then X contains at least one maximal element.
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What is a shortened version of Zorn's Lemma?
X non-empty, partially ordered set, every totally ordered subset has upper bound. X has a max.
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What is Zorn's Lemma the same as?
The axiom of choice and the well-ordered principle.
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What conditions are needed for an equivalence relation?
Reflexive, Symmetric, Transitive.
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What does reflexive mean?
For every a e A, <a,a> e R.
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What does symmetric mean?
If <a,b> e R, then <b,a> e R.
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What does transitive mean?
If <a,b> e R and <b,c> e R, then <a,c> e R.
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If R is an equivalence relation in A, then the equivalence class of any element a e A...
Denoted [a], is the set of elements to which a is related by [a] = {x : <a,x> e R}.
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What are De Morgan's Laws?
Complement swaps union and intersection; eg. (AUB)c = Ac ^ Bc.
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## Other cards in this set

### Card 2

#### Front

What does ~P mean?

Not P.

### Card 3

#### Back ### Card 4

#### Front

What does tautology mean?

#### Back ### Card 5

#### Front

What does P => Q mean?

#### Back 