Math / Discrete

QuestionWrite the converse, inverse, and contrapositive of the statement below. If he is the cowardly lion, then he wants courage.
Choose the correct converse. A. If he is not the cowardly lion, then he does not want courage. B. He is not the cowardly lion or he wants courage. C. If he wants courage, then he is the cowardly lion. D. If he does not want courage, then he is not the cowardly lion.
Choose the correct inverse. A. If he is not the cowardly lion, then he does not want courage. B. He is not the cowardly lion or he wants courage. C. If he wants courage, then he is the cowardly lion. D. If he does not want courage, then he is not the cowardly lion.
Choose the correct contrapositive. A. He is not the cowardly lion or he wants courage. B. If he wants courage, then he is the cowardly lion. C. If he is not the cowardly lion, then he does not want courage. D. If he does not want courage, then he is not the cowardly lion.

Studdy Solution

STEP 1

What is this asking? We need to rewrite a statement in three different ways: the converse, the inverse, and the contrapositive. Watch out! Don't mix up the inverse and the converse!
They're similar, but different.
Also, remember the contrapositive is like the original statement but extra fancy!

STEP 2

1. Define the statements
2. Find the converse
3. Find the inverse
4. Find the contrapositive

STEP 3

Let's define $p$ as "He is the cowardly lion" and $q$ as "He wants courage." This makes it easier to see the structure of our statement: "If $p$ , then $q$ ."

STEP 4

The converse swaps the hypothesis and the conclusion.
It's like saying, "If $q$ , then $p$ ."

STEP 5

In our case, the converse is "If he wants courage, then he is the cowardly lion." This matches option C.

STEP 6

The inverse negates both the hypothesis and the conclusion.
It's like saying, "If not $p$ , then not $q$ ."

STEP 7

So, the inverse is "If he is not the cowardly lion, then he does not want courage." This matches option A.

STEP 8

The contrapositive is the super combo!
It's the inverse of the converse (or the converse of the inverse, they're the same!). It's like saying, "If not $q$ , then not $p$ ."

STEP 9

Our contrapositive is "If he does not want courage, then he is not the cowardly lion." This matches option D.

STEP 10

Converse: C.
If he wants courage, then he is the cowardly lion. Inverse: A.
If he is not the cowardly lion, then he does not want courage. Contrapositive: D.
If he does not want courage, then he is not the cowardly lion.

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Studdy Solution

STEP 1

What is this asking? We need to rewrite a statement in three different ways: the converse, the inverse, and the contrapositive. Watch out! Don't mix up the inverse and the converse!
They're similar, but different.
Also, remember the contrapositive is like the original statement but extra fancy!

STEP 2

1. Define the statements
2. Find the converse
3. Find the inverse
4. Find the contrapositive

STEP 3

Let's define $p$ as "He is the cowardly lion" and $q$ as "He wants courage." This makes it easier to see the structure of our statement: "If $p$ , then $q$ ."

STEP 4

The converse swaps the hypothesis and the conclusion.
It's like saying, "If $q$ , then $p$ ."

STEP 5

In our case, the converse is "If he wants courage, then he is the cowardly lion." This matches option C.

STEP 6

The inverse negates both the hypothesis and the conclusion.
It's like saying, "If not $p$ , then not $q$ ."

STEP 7

So, the inverse is "If he is not the cowardly lion, then he does not want courage." This matches option A.

STEP 8

The contrapositive is the super combo!
It's the inverse of the converse (or the converse of the inverse, they're the same!). It's like saying, "If not $q$ , then not $p$ ."

STEP 9

Our contrapositive is "If he does not want courage, then he is not the cowardly lion." This matches option D.

STEP 10

Converse: C.
If he wants courage, then he is the cowardly lion. Inverse: A.
If he is not the cowardly lion, then he does not want courage. Contrapositive: D.
If he does not want courage, then he is not the cowardly lion.

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Studdy Solution

STEP 1

What is this asking? We need to rewrite a statement in three different ways: the converse, the inverse, and the contrapositive. Watch out! Don't mix up the inverse and the converse!They're similar, but different.Also, remember the contrapositive is like the original statement but *extra* fancy!

STEP 2

1. Define the statements2. Find the converse3. Find the inverse4. Find the contrapositive

STEP 3

Let's **define** ppp as "He is the cowardly lion" and qqq as "He wants courage." This makes it easier to see the structure of our statement: "If ppp, then qqq."

STEP 4

The **converse** swaps the hypothesis and the conclusion.It's like saying, "If qqq, then ppp."

STEP 5

In our case, the converse is "If he wants courage, then he is the cowardly lion." This matches option C.

STEP 6

The **inverse** negates both the hypothesis and the conclusion.It's like saying, "If not ppp, then not qqq."

STEP 7

So, the inverse is "If he is *not* the cowardly lion, then he does *not* want courage." This matches option A.

STEP 8

The **contrapositive** is the *super combo*!It's the inverse of the converse (or the converse of the inverse, they're the same!). It's like saying, "If not qqq, then not ppp."

STEP 9

Our contrapositive is "If he does *not* want courage, then he is *not* the cowardly lion." This matches option D.

STEP 10

Converse: C.If he wants courage, then he is the cowardly lion. Inverse: A.If he is not the cowardly lion, then he does not want courage. Contrapositive: D.If he does not want courage, then he is not the cowardly lion.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to rewrite a statement in three different ways: the converse, the inverse, and the contrapositive. Watch out! Don't mix up the inverse and the converse!
They're similar, but different.
Also, remember the contrapositive is like the original statement but extra fancy!

1. Define the statements
2. Find the converse
3. Find the inverse
4. Find the contrapositive

Let's define $p$ as "He is the cowardly lion" and $q$ as "He wants courage." This makes it easier to see the structure of our statement: "If $p$ , then $q$ ."

The converse swaps the hypothesis and the conclusion.
It's like saying, "If $q$ , then $p$ ."

The inverse negates both the hypothesis and the conclusion.
It's like saying, "If not $p$ , then not $q$ ."

So, the inverse is "If he is not the cowardly lion, then he does not want courage." This matches option A.

The contrapositive is the super combo!
It's the inverse of the converse (or the converse of the inverse, they're the same!). It's like saying, "If not $q$ , then not $p$ ."

Our contrapositive is "If he does not want courage, then he is not the cowardly lion." This matches option D.

Converse: C.
If he wants courage, then he is the cowardly lion. Inverse: A.
If he is not the cowardly lion, then he does not want courage. Contrapositive: D.
If he does not want courage, then he is not the cowardly lion.