Question

1.
What is the contrapositive of the following statement?

“If it does not have four legs, then it is a fish.”

If it is a fish, then it does not have four legs.
If it is not a fish, then it has four legs.
If it has four legs, then it is not a fish.
If it does not have four legs, then it is not a fish.

Answer 1

1.
What is the contrapositive of the following statement?

“If it does not have four legs, then it is a fish.” (3 points)

If it is a fish, then it does not have four legs.
* If it is not a fish, then it has four legs.
If it has four legs, then it is not a fish.
If it does not have four legs, then it is not a fish.

2.
What is the inverse of the following statement?

“If it is not Wednesday, then it is sunny.” (3 points)

If it is sunny, then it is not Wednesday.
* If it is Wednesday, then it is not sunny.
If it is not Wednesday, then it is not sunny.
If it is not sunny, then it is Wednesday.

3.
What is the converse of the following statement?

“If his shoes are clean, then he did not walk in the mud.”

(3 points)

If his shoes are not clean, then he walked in the mud.
If his shoes are clean, then he walked in the mud.
If he walked in the mud, then his shoes are not clean.
* If he did not walk in the mud, then his shoes are clean.

4.
What is the conjunction of the following two statements?

Statement 1: A midpoint divides a segment in two equal halves.
Statement 2: Supplementary angles add up to 180 degrees. (3 points)

If a midpoint divides a segment in two equal halves, then supplementary angles add up to 180 degrees.
A midpoint divides a segment in two equal halves, or supplementary angles add up to 180 degrees.
A midpoint divides a segment in two equal halves if and only if supplementary angles add up to 180 degrees.
* A midpoint divides a segment in two equal halves, and supplementary angles add up to 180 degrees.

5.
What is the disjunction of the following two statements?

Statement 1: Geometry is fun.
Statement 2: The moon comes out at night. (3 points)

Geometry is fun, and the moon comes out at night.
If geometry is fun, then the moon comes out at night.
Geometry is fun if and only if the moon comes out at night.
* Geometry is fun, or the moon comes out at night.

6.
Which statement is logically equivalent to the following conditional statement?

If it has four sides, then it is not a hexagon. (5 points)

If it does not have four sides, then it is a hexagon.
If it is not a hexagon, then it has four sides.
If it does not have four sides, then it is not a hexagon.
* If it is a hexagon, then it does not have four sides.

Answer 2

check my work, stared is the one i am picking

Answer 3

here are the term meanings GeOverview

In this lesson, you learned to find the converse, contrapositive, inverse, negation, conjunction, disjunction, conditional, and biconditional statements of a given statement.

The negation of a statement is the opposite of that statement.
The inverse of a statement is the statement in the same order with both parts negated.
The converse of a statement is the statement in the opposite order.
The contrapositive of a statement is the statement in the opposite order with both parts negated.
The conjunction of two statements is the joining of the statements with the word "and" stating that both statements must occur together.
The disjunction of two statements is the joining of two statements with the word "or" stating that both statements must occur in spite of each other. Either one may occur or the other but not both.
A conditional statement is an "if, then" statement that states if one event occurs, then the other will occur.
A biconditional statement states that both events are dependent on each other occurring.
The contrapositive is the logically equivalent statement to a conditional statement.