Given:
No variable equals 1 or 0.
To find:
The statements which is always False.
Solution:
According to identity of multiplication,
[tex]1(x)=x[/tex]
For x=2,
[tex]1(2)=2\neq 1[/tex]
So, the statement [tex]1(x)=1[/tex] always false because no variable equals 1 or 0.
Multiplication property of zero,
[tex]0(x)=0[/tex]
Commutative property of addition,
[tex]x+y=y+x[/tex]
Distributive property of multiplication over addition,
[tex]a(b+c)=ab+ac[/tex]
No variable equals 1 or 0. So, all the statements in options B, C, D are always true.
Therefore, the correct option is A.
