P1.6.4 A compound proposition is said to be symmetric if its truth value depends only on the number of basic propositions that are true, and not on which ones are true. For example, pVqV r V s is symmetric because it is false if none of the basic propositions are true, and true if one or more of them is true. (a) Write a compound proposition that is true if and only if exactly two of the basic propo- sitions p, q, r, and s are true. (b) Suppose that you have a compound proposition with k basic propositions and you know that it is symmetric. Explain how you can evaluate it using a truth table with only k +1 lines rather than 2k lines. (Hint: Some of the lines in the ordinary truth table are now guaranteed to be identical.)