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i want too create a 2-D vector of Boolean type with Size n x n . but i don't want to use two for loop to assign false to every index instead of assign directly while creating this vector. syntax is:- vector<vector<bool>> V(n,false)

but it gives me error

There is a constructor that takes a count and an element, but false is not a std::vector<bool> . You want

std::vector<std::vector<bool>> V(n, std::vector<bool>(n,false)  );
                               //   |---- inner vectors  ----|
Two disclaimer:
Use std::vector<bool> with caution. It is not like other std::vectors  (see eg Alternative to vector<bool>).
A vector of vectors is rarely the best data structure. The power of a std::vector is its data locality, however a std::vector<std::vector<T>> does not have this feature (only elements of the inner vectors are contiguous).
vector<vector> V(n,false) this gives an error because you are not declaring size of each v[i] thus, it can not assign each of v[i][j] to false.
you can use  vector<vector> v(n, vector (n, false));
Code:
#include<bits/stdc++.h>
using namespace std;
int main()
    int n;
    cin>>n;
    vector<vector<bool>> v(n, vector<bool> (n, false));
    for(int i=0;i<n;i++)
        for(int j=0;j<v[i].size();j++)
            cout<<v[i][j]<<" ";
        cout<<'\n';
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
        
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