Question

What is the negation of the following: "If it rains then I take an umbrella."

A. It rains and I don't take an umbrella.
B. If it doesn't rain then I don't take an umbrella.
C. It rains or I don't take an umbrella.
D. If I don't take an umbrella then it doesn't rain.
E. If it doesn't rain then I take an umbrella.
F. If it rains then I take an umbrella.
G. It rains or I take an umbrella.
H. If I take an umbrella then it rains.
I. It does't rain and I don't take an umbrella.
J. It doesn't rain or I take an umbrella.
K. It rains and I take an umbrella.
What is the negation of the following: "If P is a square then P is a rectangle."


A. P is a square and P is not a rectangle.
B. If P is not a square then P is not a rectangle.
C. P is not a square or P is a rectangle.
D. P is a square or P is a rectangle.
E. P is not a square and P is a rectangle.
F. If P is not a square then P is a rectangle.
G. If P is not a rectangle then P is not a square.
H. P is a square and P is a rectangle.
I. If P is a rectangle then P is a square.
J. P is a square or P is not a rectangle.
K. If P is a square then P is a rectangle.
What is the negation of the following statement: "I vote in the election and I feel enfranchised."


A. I vote in the election and I feel disenfranchised.
B. I don't vote and I feel disenfranchised.
C. I don't vote and I feel enfranchised.
D. I don't vote or I feel enfranchised.
E. I don't vote or I feel disenfranchised.
F. I vote in the election and I feel enfranchised.
G. I vote in the election or I feel enfranchised.
H. I vote in the election or I feel disenfranchised.
What is the negation of the following: "I am hungry or I eat an apple."


A. I am not hungry and I eat an apple.
B. I am hungry or I eat an apple.
C. I am hungry and I don't eat an apple.
D. I am not hungry and I don't eat an apple.
E. I am hungry and I eat an apple.
F. I am not hungry or I eat an apple.
G. I am hungry or I don't eat an apple.
H. I am not hungry or I don't eat an apple.
What is the converse of the following: "If I form a study group then I raise my grades."


A. If I form a study group then I lower my grades.
B. If I lower my grades then I work alone.
C. If I raise my grades then I work alone.
D. If I form a study group then I raise my grades.
E. If I raise my grades then I form a study group.
F. If I work alone then I lower my grades.
What is the inverse of the following: "If this triangle has two 45 degree angles then it is a right triangle."


A. If this triangle does not have two 45 degree angles then it is not a right triangle.
B. If it is a right triangle then this triangle has two 45 degree angles.
C. If it is a right triangle then this triangle does not have two 45 degree angles.
D. If this triangle has two 45 degree angles then it is not a right triangle.
E. If it is not a right triangle then this triangle does not have two 45 degree angles.
F. If this triangle has two 45 degree angles then it is a right triangle.
What is the contrapositive of the following: "If I go to Paris then I visit the Eiffel Tower."


A. If I don't go to Paris then I don't visit the Eiffel Tower.
B. If I don't visit the Eiffel Tower then I don't go to Paris.
C. If I don't visit the Eiffel Tower then I go to Paris.
D. If I visit the Eiffel Tower then I go to Paris.
E. If I don't go to Paris then I visit the Eiffel Tower.
F. If I go to Paris then I visit the Eiffel Tower.

Answer 1

The negations of the given statements are explained and provided.

Step-by-step explanation:

The negation of the statement "If it rains then I take an umbrella" is: If it rains and I don't take an umbrella. The original statement is a conditional statement, and its negation reverses the direction of the statement while adding the word "and". This means that if it rains, then I will not take an umbrella.

The negation of the statement "If P is a square then P is a rectangle" is: If P is a square and P is not a rectangle. This means that if P is a square, then it is not a rectangle.

The negation of the statement "I vote in the election and I feel enfranchised" is: I vote in the election and I feel disenfranchised. This means that if I vote in the election, then I feel disenfranchised.

The negation of the statement "I am hungry or I eat an apple" is: I am not hungry and I don't eat an apple. This means that if I am not hungry, then I don't eat an apple.

The converse of the statement "If I form a study group then I raise my grades" is: If I raise my grades then I form a study group. This means that if I raise my grades, then I have formed a study group.

The inverse of the statement "If this triangle has two 45 degree angles then it is a right triangle" is: If this triangle does not have two 45 degree angles then it is not a right triangle. This means that if the triangle does not have two 45 degree angles, then it is not a right triangle.

The contrapositive of the statement "If I go to Paris then I visit the Eiffel Tower" is: If I don't visit the Eiffel Tower then I don't go to Paris. This means that if I don't visit the Eiffel Tower, then I don't go to Paris.

Answer 2

It rains and I don't take an umbrella