Kenneth Rosen Edition 6th Exercise 1.1 Question 22 (Page No. 18)

Question

Write each of these propositions in the form “p if and only if q” in English.

• A. For you to get an A in this course, it is necessary and sufficient that you learn how to solve discrete mathematics problems.
• B. If you read the newspaper every day, you will be informed, and conversely.
• C. It rains if it is a weekend day, and it is a weekend day if it rains.
• D. You can see the wizard only if the wizard is not in, and the wizard is not in only if you can see him.

Answer 1

They are saying represent in "P if and only if Q" form. Actually double implications are commutative so "P if and only if Q" is same as "Q if and only if P".

A. You get an A in this course if and only if you learn how to solve discrete mathematics problems.
B. You will be informed if and only if you read the newspaper every day.
C. It rains if and only it is a weekend day.
D. You can see the wizard if and only if he is not in.