# (Homework Solution): 5.a Rewrite the following Pseudo Code as a propositional. 50 Points) If (x) Then (If y

5.a Rewrite the following Pseudo Code as a propositional. 50 Points) If (x) Then (If y Then w Else u Endif) Else r Endif 5.b Rewrite the following propositional in a Pseudo Code. (60 Points)

a.      Converting Pseudo code to Propositional Logic

Given:

If(x) Then

{If y Then w

Else u

Endif}

Else r

Endif

Solution:

First if clause depends on x combined with y value. That means the combination will be as follows

(if x is true and y is true then perform w) OR (x is true and y is false then perform u)

Now if x is not true then directly perform r

This can be represented as the below propositional logic:

[ ( x ^ y ) -> w ] v [ ( x ^ ~ y ) -> u ] ] v [ r ] ]

b.      Converting Propositional Logic to Pseudo code

Given:

[ (x^y) -> z ] ^ [(~x ^ y) -> w] ^[(x ^ ~y) -> u] ^ [(~x ^ ~y) -> r ]

Solution:

Here in this logic we are having 4 different clauses and each clause is must executed and to perform accordingly since each clause is combined with “and” logic instead of ”or” logic.

As these clauses combined with “and” ,else cannot applied in this context.

If (x and y) Then

z

If (Not(x) and y) Then

w

If (x and Not(y) )Then

u

If ( Not(x) and Not(y)) Then

r

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