which of the following sets is closed under multiplication A. {0, 1, 2, 4} B. {0, 1} C. {1, 2} D. none of the sets are closed un
2 answers:
A set is closed under an operation if performing that operation on the elements of the sets results in another element of the set.
In other words, you can "combine" the elements of the set, and the result is also belonging to the set.
So:
- Set A is not closed under multiplication: you can choose to perform
, and 8 is not in the set.
- Set B is closed under multiplication: the only multiplications you can perform are
. So, every possible multiplication gives 0 or 1 as result, and they both belong to the set.
- Set C is not closed under multiplication: the multiplications you can perform are
. So, the possible results are 1, 2 and 4, but 4 does not belong to the set.
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Un = a + ( n - 1 ) b
U1.000 = 2 + ( 1.000 - 1 ) 6
U1.000 = 2 + ( 999 ) 6
U1.000 = 2 + 5.994
U.1000 = 5.996
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