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ddd [48]
3 years ago
13

Is a relation always a function? Is a function always a relation? Explain.

Mathematics
1 answer:
katen-ka-za [31]3 years ago
8 0

A function is always a relation but relation is not always a function

<u>Solution:</u>

Given that, we have to explain Is a relation always a function and is a function always a relation

Note that both functions and relations are defined as sets of lists.  

In fact, every function is a relation. However, not every relation is a function.  A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y.

That is, given an element x in X, there is only one element in Y that x is related to.

For example, consider the following sets X and Y. Let me give you a relation between them that is not a function;

X = { 1, 2, 3 }

Y = { a , b , c, d }

Relation from X to Y : { (1,a) , (2, b) , (2, c) , (3, d) }

This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c

Relation from X to Y that is a function: { (1,d) , (2,d) , (3, a) }

This is a function since each element from X is related to only one element in Y. Note that it is okay for two different elements in X to be related to the same element in Y. It's still a function, it's just not a one-to-one function.

So, we can say that function is a type of relation.

Which means whatever a function occurs, it will be a relation from one set to other.

But when a relation occurs it may be a function but need not be always a function.

Hence, a function is always a relation but relation is not always a function.

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2 years ago
Write the series -25-22-19 +....for 14 terms using summation notation.
marshall27 [118]

Answer:

\sum_{n=1}^{14}(3n-28)

Step-by-step explanation:

The given series is

-25-22-19+...

The the first term of the sequence is;

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The constant difference is;

d=-22--25

d=3

The nth term of the series is

a_n=a_1+d(n-1)

a_n=-25+3(n-1)

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Using the summation notation, we can write the series as;

\sum_{n=1}^{14}(3n-28)

3 0
3 years ago
Two of the angles in a triangle measure 72° and 63°. What is the measure of the third angle?
Colt1911 [192]

Answer:

45 degrees

Step-by-step explanation:

Since all three angles would equal 180 degrees you would do 72 + 63 = 135. Then 180 - 135 = 45

hope this helps! plz mark brainliest? :)

6 0
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Your answer would be
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6 0
3 years ago
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