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enyata [817]
3 years ago
15

This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions a

nd intersections can be calculated as for any subsets. Given two relations R and S from a set A to a set B, R ∪ S = {(x, y) ∈ A ✕ B | (x, y) ∈ R or (x, y) ∈ S} R ∩ S = {(x, y) ∈ A ✕ B | (x, y) ∈ R and (x, y) ∈ S}. Let A = {−4, 4, 7, 9} and B = {4, 7}, and define relations R and S from A to B as follows. For every (x, y) ∈ A ✕ B, x R y ⇔ |x| = |y| and x S y ⇔ x − y is even. Which ordered pairs are in A ✕ B, R, S, R ∪ S, and R ∩ S? (Use set-roster notation to enter your answers.) A ✕ B = R = S = R ∪ S = R ∩ S =
Mathematics
1 answer:
Mice21 [21]3 years ago
8 0

Answer:

AXB= = {(x, y) ∈ A ✕ B| x ∈ A , y ∈  B}

R= {(x, y) ∈ A ✕ B| x R y ⇔ |x| = |y|}

S={(x, y) ∈ x A ✕ B | S y ⇔ x − y is even}

R ∪ S= {(x, y) ∈ A ✕ B | (x, y) ∈ R or (x, y) ∈ S}

R ∩ S = {(x, y) ∈ A ✕ B | (x, y) ∈ R and (x, y) ∈ S}

Step-by-step explanation:

Let A = {−4, 4, 7, 9} and B = {4, 7},

Then A X B= { (-4,4),(-4,7),(4,4),(4,7),(7,4),(7,7),(9,4),(9,7)}

AXB contains all elements of A and B such that x from A and y is from B.

AXB= = {(x, y) ∈ A ✕ B| x ∈ A , y ∈  B}

R= {(-4,4),(4,4),(7,7)}

R consists all ordered pairs where  |x| = |y|

R= {(x, y) ∈ A ✕ B| x R y ⇔ |x| = |y|}

S= { (-4,4),(4,4),(7,7)}

S={(x, y) ∈ x A ✕ B | S y ⇔ x − y is even}

S consists all ordered pairs where x-y is even.

R ∪ S, = { (-4,4),(4,4),(7,7)}

R US is a set containing subsets of both sets R and S

R ∪ S= {(x, y) ∈ A ✕ B | (x, y) ∈ R or (x, y) ∈ S}

R ∩ S=  {(-4,4),(4,4),(7,7)}

R ∩ Sis a set containing subsets only which are common between sets R and S

R ∩ S = {(x, y) ∈ A ✕ B | (x, y) ∈ R and (x, y) ∈ S}

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