In Example 2.1.4, the symbol ? was introduced to denote exclusive or, so p ? q = (p ? q)? ~(p ? q). Hence the truth table for exclusive or is as follows: a. Find simpler statement forms that are...

In Example 2.1.4, the symbol ? was introduced to denote exclusive or, so p ? q = (p ? q)? ~(p ? q). Hence the truth table for exclusive or is as follows:

a. Find simpler statement forms that are logically equivalent to p ? p and (p ? p) ? p.

b. Is (p ? q) ? r = p ? (q ? r)? Justify your answer.

c. Is (p ? q) ? r = (p ? r) ? (q ? r)? Justify your answer.

Example 2.1.4

Construct the truth table for the statement form (p ? q) ? ~(p ? q). Note that when or is used in its exclusive sense, the statement “p or q” means “p or q but not both” or “p or q and not both p and q,” which translates into symbols as (p ? q) ? ~(p ? q). This is sometimes abbreviated p ? q or p XOR q.