DMTH137 – Discrete Mathematics || Assignment

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Macquarie University

Discrete Mathematics (DMTH137)

Added on 2020-02-24

DMTH137 – Discrete Mathematics || Assignment

Macquarie University

Discrete Mathematics (DMTH137)

Added on 2020-02-24

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1 a)If you have the latest operating system then the app will install.b)Obtaining a pass in discreet maths is necessary to enrol in the Algorithm unit.c)Satisfying the Turing test is necessary for a computer to have artificial intelligence ConverseIf the app installs then you have the latest operating system.If you enrol in the algorithm unit then you have a pass in discreet maths.If the computer has an intelligence system then it satisfies the Turing test.ContrapositiveIf you do not have the latest operating system then the app will not install.If you do not obtain a pass in discreet maths then you will not enrol in the Algorithm unit.If the computer does not satisfy the Turing test then it does not have an artificial intelligence.2 a)Truth table for q ↔ (¬p ∨ ¬q)pq¬p¬q¬p ∨ ¬qq ↔ (¬p ∨¬q)TTFFFFTFFTTFFTTFTTFFTTTFb)By examining the truth table (¬p ∨ ¬q)∧q is logically equivalent to q ↔ (¬p ∨ ¬q)c)This equivalence is because the two share a similar truth table hence (¬p ∨ ¬q)∧q is the contrapositive of q ↔ (¬p ∨ ¬q)d)q↔(¬p∨¬q)=q→(¬p∨¬q)∧ (¬p∨¬q)→q¿(¬p ∨ ¬q)∧q3 a)Fb)F

DMTH137 – Discrete Mathematics || Assignment_1

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