Let 
be the set of the first 11 natural numbers. Then the number of elements in 
and the product of all elements of 
is even} is 
.
Text Solution
Verified by Experts1979
(1979)
The set 
has 11 elements.
We need to count subsets 
with 
and even product.
A product is even iff at least one element is even.
Equivalently, count complements: a product is odd if all elements are odd.
The odd numbers in 
are 
(6 elements).
Subsets of odd numbers: 
.
Among these, those with 
are all except empty set (1) and singletons (6): 
.
Total subsets with 
: 
.
Subsets with even product and 
: 2036-57 
.
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