Question

17. hy the correctness of the following program segment with the precondition and postcondition shown {x60 if x > 0 then y = 2 ** else y=(-2) *x end if {y >0} 18. Verify the correctness of the following program segment to compute x, the absolute value of x, for a nonzero number x. {r* 0 if x >= 0 then abs = r else abs = -x end if

Answer 1

17.

From the question:

if x not equal to 0

Precoditions:

(1)

if x>0

(2)

if x<0 (since x not equal ot zero dont take x as 0)

Post condition:

{y>0}

case1:

if x>0 then

let x = 1

y= 2*x = 2*1 = 2

since 2>0 the post condition y>0 is true.

case2:

else // it indicatesif x<0

let x = -3

y= (-2)*x = 2*-(-3) = 6

since 6>0 the post condition y>0 is true.

Hence proved

18.

From the question:

if x not equal to 0

Precoditions:

(1)

if x>0 (since x not equal ot zero dont take x as 0)

(2)

if x<0

Post condition:

result is |x|

case1:

if x>0 then

let x=1

abs = x = 1

since x = abs = |x| = 1 the post condition |x| is true.

case2:

else // it indicatesif x<0

let x=-1

abs = -x = -(-1) = 1

since x = -1 and abs = |x| = 1 the post condition |x| is true.

Hence proved

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