Please explain answers.

What is the negation of the following: "If it rains then I take an umbrella." A. If it doesn't rain then I don't take an umbrella. B. It rains and I take an umbrella. c. It rains or I don't take an umbrella. D. It does't rain and I don't take an umbrella. E. It doesn't rain or I take an umbrella. F. If it doesn't rain then I take an umbrella. Q. It rains or I take an umbrella. H. If I take an umbrella then it rains. I. It rains and I don't take an umbrella. J. If I don't take an umbrella then it doesn't rain. OK. If it rains then I take an umbrella. 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 I take an umbrella then it rains. C. It rains or I don't take an umbrella. D. If it doesn't rain then I don't take an umbrella. E. It doesn't rain or I take an umbrella. F. It does't rain and I don't take an umbrella. a. It rains or I take an umbrella. H. It rains and I take an umbrella. 1. If I don't take an umbrella then it doesn't rain. J. If it rains then I take an umbrella. K. If it doesn't rain then I take an umbrella. What is the negation of the following: "It rains and I take an umbrella." A. It rains and I take an umbrella. B. It does not rain or I do not take an umbrella. c. It rains or I take an umbrella. D. It does not rain or take an umbrella. E. It does not rain and I don't take an umbrella. F. It does not rain and I take an umbrella. G. It rains and I don't take an umbrella. H. It rains or I don't take an umbrella. What is the negation of the following statement: "Pis a square or P is a rectangle." A. P is a square and P is not a rectangle. B. P is not a square and P is not a rectangle. C. P is not a square or P is not a rectangle. D. P is not a square or P is a rectangle. E. P is a square or P is a rectangle. F. P is a square and P is a rectangle. A. P is a square or P is not a rectangle. H. P is not a square and P is a rectangle. What is the converse of the following: "If this triangle has two 45 degree angles then it is a right triangle." A. If this triangle has two 45 degree angles then it is a right triangle. B. If this triangle has two 45 degree angles then it is not a right triangle. C. If it is not a right triangle then this triangle does not have two 45 degree angles. D. If it is a right triangle then this triangle has two 45 degree angles. E. If this triangle does not have two 45 degree angles then it is not a right triangle. F. If it is a right triangle then this triangle does not have two 45 degree angles. What is the inverse of the following: "If n is prime then n is odd or n is 2." OA. If n is even but not 2 then n is composite. B. If n is prime then n is odd or n is 2. C. If n is odd or n is 2 then n is prime. D. If n is prime then n is even but not 2. E. If n is odd or n is 2 then n is composite. F. If n is composite then n is even but not 2. What is the contrapositive of the following: "If it rains then I take an umbrella." A. If it doesn't rain then I don't take an umbrella. B. If it doesn't rain then I take an umbrella. C. If it rains then I take an umbrella. D. If I don't take an umbrella then it doesn't rain. E. If I don't take an umbrella then it rains. OF. If I take an umbrella then it rains