Solution Found!
In Example, the symbol ® was introduced to denote
Chapter 2, Problem 46E(choose chapter or problem)
In Example 2.1.4, the symbol \(\oplus\) was introduced to denote exclusive or, so \(p \oplus q \equiv(p \vee q) \wedge \sim(p \wedge q)\). Hence the truth table for exclusive or is as follows:
a. Find simpler statement forms that are logically equivalent to \(p \oplus p\) and \((p \oplus p) \oplus p\).
b. Is \((p \oplus q) \oplus r \equiv p \oplus(q \oplus r)\)? Justify your answer.
c. Is \((p \oplus q) \wedge r \equiv(p \wedge r) \oplus(q \wedge r)\)? Justify your answer.
Text Transcription:
oplus
p oplus q equiv(p vee q) wedge sim(p wedge q)
p oplus p
(p oplus p) oplus p
(p oplus q) oplus r equiv p oplus(q oplus r)
(p oplus q) wedge r equiv(p wedge r) oplus(q wedge r)
Questions & Answers
QUESTION:
In Example 2.1.4, the symbol \(\oplus\) was introduced to denote exclusive or, so \(p \oplus q \equiv(p \vee q) \wedge \sim(p \wedge q)\). Hence the truth table for exclusive or is as follows:
a. Find simpler statement forms that are logically equivalent to \(p \oplus p\) and \((p \oplus p) \oplus p\).
b. Is \((p \oplus q) \oplus r \equiv p \oplus(q \oplus r)\)? Justify your answer.
c. Is \((p \oplus q) \wedge r \equiv(p \wedge r) \oplus(q \wedge r)\)? Justify your answer.
Text Transcription:
oplus
p oplus q equiv(p vee q) wedge sim(p wedge q)
p oplus p
(p oplus p) oplus p
(p oplus q) oplus r equiv p oplus(q oplus r)
(p oplus q) wedge r equiv(p wedge r) oplus(q wedge r)
ANSWER:Step 1 of 4
(a) The exclusive or is true, if is true or is true (but not both).