Question

What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached?

a) if $\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{=}\mathbf{3}$then $\mathbf{x}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{1}$
b) if $\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{3}\mathbf{)}$OR $\mathbf{(}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{=}\mathbf{3}\mathbf{)}$then $\mathbf{x}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{1}$
c) if $\mathbf{(}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{3}\mathbf{=}\mathbf{5}\mathbf{)}$AND $\mathbf{(}\mathbf{3}\mathbf{x}\mathbf{+}\mathbf{4}\mathbf{=}\mathbf{7}\mathbf{)}$then $\mathbf{x}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{1}$
d) if $\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{2}\mathbf{)}$XOR $\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{=}\mathbf{3}\mathbf{)}$then $\mathbf{x}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{1}$
e) if x < 2 then$\mathbf{x}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{1}$

Short answer

a) x = 2

b) x = 1

c) x = 2

d) x = 1

e) x = 2

Step-by-step solution

Definition of Statement

Mathematical statement is a sentence that is either true or false.

Value of x in a)

We write given expression as,

$x+2=3$

Giventhat initially x = 1,

Therefore, substitute 1 for x in the below given equation,

x = x+1

= 1+1.

=2

Hence, x = 2.

Value of x in b)

We write given expression,

Given that x = 1,

$$\begin{gathered} \mathrm{x}+1=1+1 \\ \ne 3 \end{gathered}$$

$$\begin{gathered} 2\mathrm{x}+2=2+2 \\ \ne 3 \end{gathered}$$

False or false gives false.

Hence, x = 1

Value of x in c)

We write given expression as,

Given that x = 1,

$$\begin{gathered} 2x+3=2+3 \\ =5 \end{gathered}$$

$$\begin{gathered} 3x+4=3+4 \\ =7 \end{gathered}$$

True and true gives true.

Hence, x = 2.

Value of x in d)

We write given expression,

Given that x = 1,

$\mathrm{x}+1=2$

$\mathrm{x}+2=3$

True Ex-Or True gives false.

Hence, x = 1

Value of x in e)

We write given expression,

Given that x = 1,

Here 1 < 2

Hence,x = 2.