Which of the following is my assumption in order to do a proof by CONTRAPOSITIVE?

Question

Consider the following statement: If an m x n matrix A is the zero matrix, then it is made entirely of zeros and makes students happy."

Which of the following is my assumption in order to do a proof by CONTRAPOSITIVE?

A. Assume A is made entirely of zeros and doesn't make students happy.

B. Assume A is not the m x n zero matrix.

C. Assume A is the m x n zero matrix.

D. Assume A is not made entirely of zeros and doesn't make students happy.

E. Assume A is not made entirely of zeros or doesn't make students happy.

Answer 1

A then B. Contrapositive is not B then not A.

A - made zeros

B - students happy

Students not happy, then A not made of zeroes

so D