contestada

1. Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4}. Find a. R1 ∪ R2 b. R1 ∩ R2 c. R1 – R2 d. R2 – R1

Respuesta :

vlatkostojanovic

Answer:

a) R1 ∪ R2={(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}

b)  R1 ∩ R2= {(1, 2), (2, 3), (3, 4)}

c) R1 – R2= ∅

d) R2 – R1= {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}

Step-by-step explanation:

We know that:

R1 = {(1, 2), (2, 3), (3, 4)}

R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}

Therefore, we get  

a) R1 ∪ R2={(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)}

b)  R1 ∩ R2= {(1, 2), (2, 3), (3, 4)}

c) R1 – R2= ∅

d) R2 – R1= {(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)}

aksnkj

The value of the required union, intersections, and subtraction will be [tex]R_1 \cup R_2=\{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)\}[/tex], [tex]R_1 \cap R_2=\{(1, 2), (2, 3), (3, 4)\}[/tex], [tex]R_1 -R_2=\phi[/tex], and [tex]R_2 - R_1=\{(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)\}[/tex].

Given information:

[tex]R_1 = \{(1, 2), (2, 3), (3, 4)\}[/tex] and [tex]R_2 = \{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)\}[/tex] be relations from {1, 2, 3} to {1, 2, 3, 4}.

a.

The value of [tex]R_1 \cup R_2[/tex] will be,

[tex]R_1 \cup R_2=\{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)\}[/tex]

b.

The value of [tex]R_1 \cap R_2[/tex] will be,

[tex]R_1 \cap R_2=\{(1, 2), (2, 3), (3, 4)\}[/tex]

c.

The value of [tex]R_1 -R_2[/tex] will be,

[tex]R_1 -R_2=\{(1, 2), (2, 3), (3, 4)\}- \{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)\}\\=\phi[/tex]

d.

The value of [tex]R_2 - R_1[/tex] will be,

[tex]R_2 - R_1=\{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)\}-\{(1, 2), (2, 3), (3, 4)\}\\=\{(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)\}[/tex]

Therefore, the value of the required union, intersections, and subtraction will be [tex]R_1 \cup R_2=\{(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)\}[/tex], [tex]R_1 \cap R_2=\{(1, 2), (2, 3), (3, 4)\}[/tex], [tex]R_1 -R_2=\phi[/tex], and [tex]R_2 - R_1=\{(1, 1), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)\}[/tex].

For more details, refer to the link:

https://brainly.com/question/15126489

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