Let S = 1 ,   2 ,   3 ,   … . , 100 , then number of non-empty subsets A of S such that the product of elements in A is even is :

Question

Let S = 1 , &#160; 2 , &#160; 3 , &#160; &#8230; . , 100 , then number of non-empty subsets A of S such that the product of elements in A is even is :

Aicharya · Accepted Answer

As we know that the product of numbers is even when at least one of the number must be even.

Hence total subsets of $A$ in which product of numbers is even $=$ Total subsets $-$ total subsets in which all the elements are odd

$= 2^{100} - 2^{50} = 2^{50} (2^{50} - 1)$ .

Let S = 1 ,   2 ,   3 ,   … . , 100 , then number of non-empty subsets A of S such that…

Solution

Let S = 1 , &#160; 2 , &#160; 3 , &#160; &#8230; . , 100 , then number of non-empty subsets A of S such that…

Solution

Let S = 1 , 2 , 3 , … . , 100 , then number of non-empty subsets A of S such that…