QuestionWrite the converse, inverse, and contrapositive of the statement below.
If you look down, then you are on the roof.
Choose the correct converse.
A. If you do not look down, then you are not on the roof.
B. If you are on the roof, then you look down
C. If you are not on the roof, then you do not look down.
D. You do not look down or you are on the roof.
Studdy Solution
STEP 1
What is this asking?
We need to rewrite the given "if-then" statement in three different ways: the converse, inverse, and contrapositive, and then pick the correct converse from the choices.
Watch out!
Don't mix up the converse, inverse, and contrapositive!
They each have a specific way to rewrite the original statement.
STEP 2
1. Find the Converse
2. Find the Inverse
3. Find the Contrapositive
4. Identify the Correct Converse
STEP 3
The **converse** of an "if-then" statement swaps the hypothesis and conclusion.
Our original statement is "If you look down, then you are on the roof." So, the hypothesis is "you look down" and the conclusion is "you are on the roof."
STEP 4
Let's **swap** them!
The converse becomes: "If you are on the roof, then you look down."
STEP 5
The **inverse** of a statement negates both the hypothesis and the conclusion.
Remember, our original statement is "If you look down, then you are on the roof."
STEP 6
Negating both parts, we get: "If you do *not* look down, then you are *not* on the roof."
STEP 7
The **contrapositive** of a statement both swaps *and* negates the hypothesis and conclusion.
It's like doing the converse and the inverse combined!
Again, our original statement is "If you look down, then you are on the roof."
STEP 8
Let's **swap and negate**: "If you are *not* on the roof, then you do *not* look down."
STEP 9
We found the converse in the first step: "If you are on the roof, then you look down."
STEP 10
Looking at the choices, option B matches our converse perfectly!
STEP 11
The converse is "If you are on the roof, then you look down." The inverse is "If you do not look down, then you are not on the roof." The contrapositive is "If you are not on the roof, then you do not look down." The correct answer choice for the converse is B.
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