Please help prove these and state equivlance/inference laws used a. ¬(p O q) = (p → q)b. (р^ -9) — (p Өr) + -руqvar(p → q) v (p → r) → p → (q v r)C.

To prove the following using equivalence law: a. ¬(p⊕q)⇔(p↔q) b. (p∧¬q)→(p⊕q)⇔¬p∨q∨¬r c.…

Answered: а. — (р @ q) + (р+q) b. (p ^ ¬q) → (p O…

Math

Algebra

а. — (р @ q) + (р+q) b. (p ^ ¬q) → (p O r) → ¬p V q V ¬r с. (р — q)v(р r) —ръ(qvr) С.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Please help prove these and state equivlance/inference laws used

a. ¬(p O q) = (p → q)
b. (р^ -9) — (p Өr) + -руqvar
(p → q) v (p → r) → p → (q v r)
C.

Expert Solution

Step 1

To prove the following using equivalence law:

$(a) . \neg (p \oplus q) \Leftrightarrow (p \leftrightarrow q)$

$(b) . (p \land \neg q) \to (p \oplus q) \Leftrightarrow \neg p \lor q \lor \neg r$

$(c) . (p \to q) \lor (p \to r) \Leftrightarrow p \to (q \lor r)$

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