Problem 3:thatUse the logical equivalences established in Theorem 2.1.1 as well as the properties of conditional statements to provethat the three statements below are all logically equivalent (Cite each equivalence used, and only use one at a time.)(a) p → q V r(b) p ^ ~q – r(c) p ^~ r – qProblem 4: Use the result of Problem 3 to write two other statements logically equivalent to the statement "If an integer n is prime, then n is even or n > 3".(Write these in the same English style as the given statement.)

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Description: Problem 3:thatUse the logical equivalences established in Theorem 2.1.1 as well as the properties of conditional statements to provethat the three statements below are all logically equivalent (Cite each equivalence used, and only use one at a time.

Logical equivalence1. Associative laws;(p∧q)∨r≡p∨(q∨r)(p∧q)∧r=p∧(q∧r)2. commutative…

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Use the logical equivalences established in Theorem 2.1.1 as well as the properties of conditional statements to prove that the three statements below are all logically equivalent (Cite each equivalence used, and only use one at a time.) (а) р —qVr (b) p ^ ~q -→ r (c) p ^~ r → q Problem 4: Use the result of Problem 3 to write two other statements logically equivalent to the statement "If an integer n is prime, then n is even or n> 3' (Write these in the same English style as the given statement.)

Use the logical equivalences established in Theorem 2.1.1 as well as the properties of conditional statements to prove that the three statements below are all logically equivalent (Cite each equivalence used, and only use one at a time.) (а) р —qVr (b) p ^ ~q -→ r (c) p ^~ r → q Problem 4: Use the result of Problem 3 to write two other statements logically equivalent to the statement "If an integer n is prime, then n is even or n> 3' (Write these in the same English style as the given statement.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Problem 3:
that
Use the logical equivalences established in Theorem 2.1.1 as well as the properties of conditional statements to prove
that the three statements below are all logically equivalent (Cite each equivalence used, and only use one at a time.)
(a) p → q V r
(b) p ^ ~q – r
(c) p ^~ r – q
Problem 4: Use the result of Problem 3 to write two other statements logically equivalent to the statement "If an integer n is prime, then n is even or n > 3".
(Write these in the same English style as the given statement.)

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