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Activity 2.2B - MMW

The document defines a relation C from R to R where (x, y) is in C if x^2 + y^2 = 1. It then evaluates whether certain points are in C. The domain of C is {0, 1} and the co-domain is {-1, 0}. It also evaluates compositions of various functions, determining if operations like f + g are binary operations based on their outputs remaining within the defined sets.

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Angelina Boniog
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193 views1 page

Activity 2.2B - MMW

The document defines a relation C from R to R where (x, y) is in C if x^2 + y^2 = 1. It then evaluates whether certain points are in C. The domain of C is {0, 1} and the co-domain is {-1, 0}. It also evaluates compositions of various functions, determining if operations like f + g are binary operations based on their outputs remaining within the defined sets.

Uploaded by

Angelina Boniog
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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1.

Define a relation C from R to R as follows: for any (x, y) ∈ R x R, (x, y) ∈ C


meaning that x2 + y2 = 1.
a. Is (1,0) ∈ C? Is (0,0) ∈ C? Is -2 C 0? Is 0 C (-1)?
Yes, (1,0) ∈ C
No, (0,0) ∉ C
No, -2 is not related to 0
Yes, 0 is related (-1)
b. What are the domain and the co-domain of C?
Domain: {0, 1}
Co-domain: {-1, 0}

2. If f(x) = 2x2 and g(x) = 3x + 1, evaluate the following:


a. (f + g) (x) = (2x2) + (3x+1)
= 2x2 + 3x + 1
b. (f • g) (x) = (2x2) • (3x+1)
= 6x3 + 2x2
f ( ) 2 x2
c. ()
g
x=
3 x +1
d. (g ○ f) (x) = 3(2x2) + 1
= 6x2 + 1

3. Tell whether the following is a binary operation or not.


a. G ∈ Z defined * by a * b = a2 – b2 for all set a, b ∈ Z.
Explanation: It is a Binary Operation because any
number substituted to, as a value of a and b will have a
positive or negative value which is an element of real
numbers.
b. G ∈ N, defined * by a * b = 2 + 3ab for all set a, b ∈ N.
Explanation: It is also a Binary Operation since any
natural number present in a set without zero,
substituted to as a value of a and b will be resulting to
the natural numbers present in the set without zero.

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