Problem

In Example, the symbol ® was introduced to denote exclusive or, so Hence the truth table...

In Example, the symbol ® was introduced to denote exclusive or, so Hence the truth table for exclusive or is as follows:

p	q
T	T	F
T	F	T
F	T	T
F	F	F

a. Find simpler statement forms that are logically equivalent to .
b. Is Justify your answer.
c. Is Justify your answer.

Example

Truth Table for Exclusive Or

Construct the truth table for the statement form 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 . This is sometimes abbreviated or p XOR q.

Solution Set up columns labeled p, q, and . Fill in the p and q columns with all the logically possible combinations of T’s and F’s. Then use the truth tables for ∨ and ∧ to fill in the p ∨ q and p ∧ q columns with the appropriate truth values. Next fill in the ∼(p ∧ q) column by taking the opposites of the truth values for p ∧ q. For example, the entry for ∼(p ∧ q) in the first row is F because in the first row the truth value of p ∧ q is T. Finally, fill in the (p ∨ q) ∧ ∼(p ∧ q) column by considering the truth table for an and statement together with the computed truth values for p ∨ q and ∼(p ∧ q). For example, the entry in the first row is F because the entry for p ∨ q is T, the entry for ∼(p ∧ q) is F, and an and statement is false unless both components are true. The entry in the second row is T because both components are true in this row.