非常遗憾，没有弄懂题主“按位或”一题的思路。
我将代码调成如下形式以便于查看内部的运算步骤

#include<cstdio>
#include<iostream>
#include<bitset>
using namespace std;
int p[10] = {0};
int mx = 10 ;
int q ;
int main()
{
    scanf("%d",&q) ;
    while(q--) {
        int op , x;scanf("%d%d",&op,&x) ;
        if(op == 1) {
            bitset<4> b_x(x);
            cout << "x = " << b_x << endl;
            if(p[x] == x){
                printf("p[%d] == %d", x, x); 
                continue;
            } 
            int s = mx ^ x;
            bitset<4> b_s(s); 
            bitset<4> b_mx(mx);
            cout << "mx ^ x = "<< b_mx << " ^ " << b_x << " = " << b_s << endl;
            for(int i = s ; i ; i = (i - 1) & s) {
                bitset<4> b_i(i);
                bitset<4> b_pbefore(p[i ^ x]);
                bitset<4> b_ix(i ^ x);
                p[i ^ x] |= x ;
                bitset<4> b_pafter(p[i ^ x]);
                cout << "p[i ^ x] = p[i ^ x] | x ="<< "p[ "<< b_ix<<" ] | "<< b_x <<" = " << "p[ "<< (i ^ x) <<" ] | "<< x <<" = "<< b_pbefore << " | " << b_x << " = " << b_pafter<< endl;
            }
            p[x] = x;
        }
        else {
            if(p[x] == x) puts("YES") ;
            else puts("NO");
        }
    }
    return 0;
}

然后得到了如下输出：

10
1 4
x = 0100
mx ^ x = 1010 ^ 0100 = 1110
p[i ^ x] = p[i ^ x] | x =p[ 1010 ] | 0100 = p[ 10 ] | 4 = 1001 | 0100 = 1101
p[i ^ x] = p[i ^ x] | x =p[ 1000 ] | 0100 = p[ 8 ] | 4 = 0000 | 0100 = 0100
p[i ^ x] = p[i ^ x] | x =p[ 1110 ] | 0100 = p[ 14 ] | 4 = 0000 | 0100 = 0100
p[i ^ x] = p[i ^ x] | x =p[ 1100 ] | 0100 = p[ 12 ] | 4 = 0000 | 0100 = 0100
p[i ^ x] = p[i ^ x] | x =p[ 0010 ] | 0100 = p[ 2 ] | 4 = 0000 | 0100 = 0100
p[i ^ x] = p[i ^ x] | x =p[ 0000 ] | 0100 = p[ 0 ] | 4 = 0000 | 0100 = 0100
p[i ^ x] = p[i ^ x] | x =p[ 0110 ] | 0100 = p[ 6 ] | 4 = 0000 | 0100 = 0100
2 5
NO
1 9
x = 1001
mx ^ x = 1010 ^ 1001 = 0011
p[i ^ x] = p[i ^ x] | x =p[ 1010 ] | 1001 = p[ 10 ] | 9 = 1011 | 1001 = 1011
p[i ^ x] = p[i ^ x] | x =p[ 1011 ] | 1001 = p[ 11 ] | 9 = 0000 | 1001 = 1001
p[i ^ x] = p[i ^ x] | x =p[ 1000 ] | 1001 = p[ 8 ] | 9 = 0100 | 1001 = 1101
1 15
x = 1111
mx ^ x = 1010 ^ 1111 = 0101
p[i ^ x] = p[i ^ x] | x =p[ 1010 ] | 1111 = p[ 10 ] | 15 = 1010 | 1111 = 1111
p[i ^ x] = p[i ^ x] | x =p[ 1011 ] | 1111 = p[ 11 ] | 15 = 1001 | 1111 = 1111
p[i ^ x] = p[i ^ x] | x =p[ 1110 ] | 1111 = p[ 14 ] | 15 = 0100 | 1111 = 1111
2 4
YES
1 11
x = 1011
mx ^ x = 1010 ^ 1011 = 0001
p[i ^ x] = p[i ^ x] | x =p[ 1010 ] | 1011 = p[ 10 ] | 11 = 1101 | 1011 = 1111
2 10
NO
2 7
NO
2 9
YES
2 4
YES

我不清楚int s = mx ^ x;一句的含义。
不清楚如下循环的含义

for(int i = s ; i ; i = (i - 1) & s) {
    p[i ^ x] |= x ;
}

以及上述循环为什么在4输入时，将p[10, 8, 14, 12, 2, 0, 6]依次赋值，后者的值是前者对x的异或。