# Math Help - Answer plzzzz

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+
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2. Originally Posted by Peacewanters007
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+
****!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 $S = \{0, 1 \}$

Then let's do +:
$0 + 0 = 0 \in S$

$0 + 1 = 1 \in S$

$1 + 0 = 1 \in S$

$1 + 1 = 2 \not \in S$

So S is not closed under +.

Now let's look at *:
$0 * 0 = 0 \in S$

$0 * 1 = 0 \in S$

$1 * 0 = 0 \in S$

$1 + 1 = 1 \in S$

So S is closed under *.

-Dan