Relations and Functions

If set A contains m elements and set B contains n elements, then the set A x B will have

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m+n

m.n

m-n

m.m

n.n

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Any subset of ordered pairs in A x B is called a relation from

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A to B

B to A

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A x B

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Let A = {1, 2, 3} and B = {2, 4}, then A x B =

{(2,1), (4,1), (2,2), (4,2), (2,3), (4,3)}

{(2,1), (4,1), (2,2), (4,2), (2,3)}

{(1,2), (1,4), (2,2), (2,4), (3,2), (3,4)}

{(1,2), (1,4), (2,2), (2,4), (3,2)}

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Function from A to B

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A collection of ordered pairs (from the set A x B) constitute a special relation from A to B, which is called a function from A to B if we select the ordered pairs in such a way that:

their first elements constitute the entire set A

no two distinct pairs have the same first element

their second elements constitute the entire set B

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Relations from A to B

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Let A = {1, 2, 3, 4} and B = {2, 4, 5}

The following are all possible relations from A to B

R₁ = {(1, 2), (1, 5), (2, 2), (3, 4), (3, 5), (4, 5)}
R₂ = {(1, 4), (4, 2), (4, 5)}
R₃ = {(3, 2), (3, 4), (3, 5), (1, 4)}
R₄ = {(1, 4), (2, 5), (3, 2), (4, 4)}
R₅ = {(1, 2), (2, 5), (3, 4), (4, 4)}

True

False

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Product with empty set

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Let A = {1, 2, 3}, B = ∅, Then A x B =

{(1,1), (2,2), (3,3)}

∅

{1, 2, 3}

{(1,∅),(2,∅),(3,∅)}

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Domain of a Relation

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In any relation (in the form of a set of ordered pairs), the set consisting of the ________ element of each pair constitutes the domain of the relation.

first

second

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Given a domain of R, tell if it is a function

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Let A = {1, 2, 3, 4} and B = {2, 4, 5}

The following are all possible relations from A to B

R₁ = {(1, 2), (1, 5), (2, 2), (3, 4), (3, 5), (4, 5)}
R₂ = {(1, 4), (4, 2), (4, 5)}
R₃ = {(3, 2), (3, 4), (3, 5), (1, 4)}
R₄ = {(1, 4), (2, 5), (3, 2), (4, 4)}
R₅ = {(1, 2), (2, 5), (3, 4), (4, 4)}

Which of these relations represent a function

R₁ (1) a function
R₂ (2) a function
R₃ (3) a function
R₄ (4) a function
R₅ (5) a function

Please drag and drop the selected option in the right place or type it instead

represents

does not represent

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If set A contains m elements and set B contains n elements, then the set A x B will have

Correct Answer

Explanation

Any subset of ordered pairs in A x B is called a relation from

Correct Answer

Explanation

A x B

Correct Answer

Explanation

Function from A to B

Correct Answer

Explanation

Relations from A to B

Correct Answer

Explanation

Product with empty set

Correct Answer

Explanation

Domain of a Relation

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Explanation

Given a domain of R, tell if it is a function

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Explanation

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