2. (10 points) (Multiple choices questions) (Necessary and sufficient conditions) In the
following 5 paired statements, let p be the first statement and q the second.
(1) it is Valentine's Day; It is a holiday.
(2) She is named; her name is Alice.
(3) The square matrix A has the reverse matrix;|A| is not equal to zero.
(4) A is a square matrix; A is an identity matrix.
(5) a + b = 2; a = 1, b = 1.
Indicate for each case which of the following answers is/are true?
(a) p constitutes a necessary condition of q;
(b) constitutes a necessary condition of p;
(c) p constitutes a sufficient condition of q;
(d) q constitutes a sufficient condition of p;