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juin [17]
3 years ago
13

What is converse inverse and contrapostive?

Mathematics
1 answer:
Rufina [12.5K]3 years ago
7 0

<span>rhythm of the falling rain answered 6 year<span>Given an if-then statement "if p, then q", we can create three related statements: 


A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause. 

For instance, “If it rains, then they will cancel school.” 
“It rains, “is the hypothesis. 
“They will cancel school,” is the conclusion. 

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. 

The converse of “If it rains, then they will cancel school.” is 
“If they cancel school, then it rains.” 

To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. 

The inverse of “If it rains, then they will cancel school” is “If it does not rain, then they do not cancel school.” 

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. 

The contrapositive of “If it rains, then they will cancel school” is “If they do not cancel school, then it does not rain.” 

Summary: 
Statement If p, then q. 
Converse If q, then p. 
Inverse If not p, then not q. 
Contrapositive If not q, then not p. 

If the statement is true, then the contrapositive is also logically true. If the converse is true, then the inverse is also logically true. 

Example: 
Statement If a person is 18 years old, then he is a legal adult. 
Converse If a person is a legal adult, then he is 18 years old. 
Inverse If a person is not 18 years old, then he is not a legal adult. 
Contrapositive If a person is not a legal adult, then he is not 18 years old.</span></span>
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Answer:

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Answer:

D: {(-5, -4, 2, 2, 5)}

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The relation is NOT a function.

Step-by-step explanation:

By definition:

A relation is any set of ordered pairs, which can be thought of as (input, output).

A function is a <em><u>relation</u></em> in which no two ordered pairs have the same first component (domain/input/x value) and different second components  (range/output/y value).

Looking at the given points in your graph, and in listing down the domain and range, we can infer that the relation is not a function because there is an x-value (2) that has two corresponding y-values: (2, 4) (2, 1).

Another way to tell if a given set of points in a graph represents a function by doing the "Vertical line test." The graph of an equation represents y as a function of x if and only if no vertical line intersects the graph more than once. Looking at the attached image, I drew a vertical line over points (2, 4) (2, 1). The vertical line intersects the two points, which fails the vertical line test. This is an indication that the given relation is not a function.

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