Question

For problems 2 - 4, you will need to know the following variations to the conditional. The Converse of $p \rightarrow q$ is $q \rightarrow p$ The Inverse of $p \rightarrow q$ is $\sim p \rightarrow \sim q$ The Contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$ 2. Write the contrapositive of the following statement and use the contrapositive to determine whether the given statement is true or false. If $2x + 5 = 11$, then $x \neq 4$.

          For problems 2 - 4, you will need to know the following variations to the conditional.
The Converse of $p \rightarrow q$ is $q \rightarrow p$
The Inverse of $p \rightarrow q$ is $\sim p \rightarrow \sim q$
The Contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$
2. Write the contrapositive of the following statement and use the contrapositive to determine
whether the given statement is true or false.
If $2x + 5 = 11$, then $x \neq 4$.

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For problems 2 - 4, you will need to know the following variations to the conditional.
The Converse of p → q is q → p
The Inverse of p → q is ∼ p →∼ q
The Contrapositive of p → q is ∼ q →∼ p
2. Write the contrapositive of the following statement and use the contrapositive to determine
whether the given statement is true or false.
If 2x + 5 = 11, then x ≠ 4.

Added by Virginia R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Natalie Belcher

10/14/2022

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For problems 2-4, you will need to know the following variations to the conditional. The Converse of p->q is q->p The Inverse of p->q is ∼p->∼q The Contrapositive of p->q is ∼q->∼p 2. Write the contrapositive of the following statement and use the contrapositive to determine whether the given statement is true or false. If 2x+5=11, then x!=4. If2x+5=11,then x4. The Contrapositive of p -> q is ~ q -> ~ p The Inverse of p->q is ~ p ->~ q The Converse of p-> q is q -> p For problems 2 -- 4, you will need to know the following variations to the conditional.

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Transcript

00:01 If i play ice hockey, so i play hockey, that's the hypothesis, then i will be famous.

00:08 So that is the conclusion.

00:10 I will be famous.

00:12 So converse is where you switch them.

00:15 So that is going to be if i am famous, then i play ice hockey.

00:35 Okay, inverse is where you negate.

00:38 So if i do not play hockey, sorry, yes.

00:47 If i do not play ice hockey, then i will not be famous.

02:56 Okay, change the type -ed -out so you can read them better.

02:59 So contrapositive is where you switch it and negate it.

03:03 So it's kind of like a combination of converse and inverse.

03:06 So i'm switching hypothesis conclusion and negating them.

03:09 So if i am not famous, then i do not play ice hockey.

03:16 Okay, if it rains this season, that's my hypothesis, then we will have a good harvest.

03:27 That is the conclusion.

03:30 Okay, so for converse, i am switching them.

03:36 If we have a good harvest, then it has rained this season.

03:59 Okay, inverse, we're negating them.

04:02 So if it does not rain this season, then we will.

04:17 Not have a good harvest.

04:30 Contrapositive or negating and switching...

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