## Hiatus and another three rounds of MAT422

Perhaps it is too late, but we’ve completely forgotten ever setting up this blog for this course!

One whole semester went by. Exam is over. Time to look at the scripts.

## Solutions to Exercises 6 and 7

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## Protected: Solution to Exercise 4

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## Protected: Exercises 5, 6, 7 and 8

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## Protected: Exercise 4

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## Logic: Distributive rules

Distributive rules:

i) $p \vee (q\wedge r) = (p\vee q)\wedge (p\vee r)$
ii) $p \wedge (q\vee r) = (p\wedge q)\vee (p\wedge r)$

Proof: i)

 $p$ $q$ $r$ $q\wedge r$ $p\vee (q\wedge r)$ $p\vee q$ $p\vee r$ $(p\vee q)\wedge (p\vee r)$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $0$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $1$ $0$ $1$ $0$ $1$ $1$ $1$ $1$ $0$ $0$ $1$ $0$ $0$ $0$ $1$ $0$ $1$ $1$ $0$ $0$ $1$ $1$ $1$ $1$ $0$ $1$ $0$ $0$ $0$ $1$ $0$ $0$ $1$ $0$ $0$ $0$ $1$ $1$ $1$ $1$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $0$

Can you see that the values of $p \vee (q\wedge r)$ and $(p\vee q)\wedge (p\vee r)$ are exactly the same line by line? This means they are logically equivalent.

ii) Exercise

Posted in Logic and Proving Techniques | 2 Comments