Hello,
Can anyone help me simplifying this term?
a AND (a xor b)
I know that I can write it like this:
(a AND not b) OR (not a AND b)
But how to simplify further? Would be grateful for any help. Thanks!
Hello, shadow147!
I'll let you supply some of the reasons . . .
Simplify: .a AND (a XOR b)
. . $\displaystyle \begin{array}{ccc}a \cap \bigg[(a \cap b') \cup (a' \cap b)\bigg] & & \text{Given} \\ \\ \bigg[ a\cap (a \cap b')\bigg] \cup \bigg[a \cap(a'\cap b)\bigg] && \text{Distributive} \\ \\ \bigg[(a\cap a) \cap b'\bigg] \cup \bigg[(a\cap a') \cap b\bigg] & & \text{Associative}\end{array}$
. . . . . $\displaystyle \begin{array}{c}(a\cap b') \cup (f \cap b) \\ \\(a \cap b') \cup f \\ \\ a \cap b' \end{array}$
Awesome, much appreciated, thank you!
Just one question:
$\displaystyle
a\cap a'
$
Thats = 0 isn't it? Why did you replace it with f? And at the end you got
$\displaystyle
a\cap b' \cup f
$
Why is it possible to ignore the f and say that
$\displaystyle
(a\cap b')
$
is the result?