Question

2. (8 points) A sequence of statements is listed below: b = (a+4)/2 c=2* b-5 d = 3*c+ 7 {d>4} calculate the weakest precondition of the sequence.

Answer 1

b=(a+4)/2

c=2*b-5

d=3*c+7

Substitute the right hand side of the d=3*c+7  in the postcondition given(d>=4) to get a postcondition for the assignment (c=2*b+5)  then substitute the right hand side of the assignment(c=2*b+5) in that postcondition to get the precondition

Repeat this for every statement in the sequence.The final precondition is the weakest precondition for the sequence.

substitute  d>=4 we get

3*c+7>=4

=>3*c>=-3

=>c>=-1

substitute c>=-1

=>2*b-5>=-1

=>2*b>=4

=>b>=2

now substitute b>=2

(a+4)/2>=2

a+4>=4

a>=0

hence preconditions of each statements are

b=(a+4)/2=>{a>=0}

{b>=2}

c=2*b-5

{c>=-1}

d=3*c+7

{d>=4}

Therefore the weakest precondition of the total sequence is a>=0

if u understand this upvote else post a comment