1:Set {0}have closure property or not w.r.t both * and+
2:{0,1} have closure property or not w.r.t both * and+
please explain your answer
****!THANKS 4 SPENDING YOUR PRECIOUS TIME!****
I'll do number 2, you do number 1.
In order for a set S to be closed under some operation #, we require that the operation a#b is in S for all a, b belonging to S.
Define $\displaystyle S = \{0, 1 \}$
Then let's do +:
$\displaystyle 0 + 0 = 0 \in S$
$\displaystyle 0 + 1 = 1 \in S$
$\displaystyle 1 + 0 = 1 \in S$
$\displaystyle 1 + 1 = 2 \not \in S$
So S is not closed under +.
Now let's look at *:
$\displaystyle 0 * 0 = 0 \in S$
$\displaystyle 0 * 1 = 0 \in S$
$\displaystyle 1 * 0 = 0 \in S$
$\displaystyle 1 + 1 = 1 \in S$
So S is closed under *.
-Dan