b) What is the value of x after each of these statements is encountered in a computer program, if x =3 before the statement is reached? i) if x +2=5 then x := 3*x +5 ii) if (x +1=4) OR (2x +2=3) then x := x +1 iii) if (2x +3=5) AND (3x +4=13) then x := x^2 +x+7 iv) if (x +1=4) XOR (x +2=5) then x := x +1 v) if x<2 then x := 4*x^3

Let $x:=3.$

i) Since $3+2=5$ is a true statement, after the command "if x +2=5 then x := 3*x +5" the value of $x$ is $3\cdot 3+5 =14.$

Answer: $x = 14$

ii) Since $3+1=4$ is a true statement, the statemant $(3 +1=4) \text{ OR }(2\cdot 3 +2=3)$ is also true, and thus after the command "if (x +1=4) OR (2x +2=3) then x := x +1" the value of $x$ is $3+1=4$

Answer: $x = 4$

iii) Since $2\cdot 3+3=5$ is a false statement, the statement "($2\cdot 3 +3=5$ ) AND ($3\cdot 3 +4=13$ )" is also false, and thus after the command "if (2x +3=5) AND (3x +4=13) then $x := x^2 +x+7$ " the value of $x$ does not change.

Answer: $x = 3$

iv) Since $3+1=4$ is a true statement and $3+2=5$ is a true statement, the statement

"($3 +1=4$ ) XOR ($3 +2=5$ )" is false, and thus after the command "if (x +1=4) XOR (x +2=5) then x := x +1" the value of $x$ does not change.

Answer: $x = 3$

v) Since $3<2$ is a false statement, after the command "if $x<2$ then $x := 4\cdot x^3$ " the value of $x$ does not change.

Answer: $x = 3$