The domain is the members of a chess club. The predicateB(x, y)means that personxhas beatenpersonyat some point in time. Give a logical expression equivalent to the following English statements. You can assume that it is possible for a person to beat himself or herself.8(a) Sam has been beaten by someone.8(b) No one has ever beaten Nancy.8(c) Everyone has won at least one game.8(d) Josephine has beaten everyone else.8(e) Nancy has beaten exactly one person.

Acommon algorithm for converting a decimal number to binary is to repeatedly divide the decimal number by 2 and save the remainder. this division is continued until the result is zero. then, each of the remainders that have been saved are used to construct the binary number. write a recursive java method that implements this algorithm. it will accept a value of int and return a string with the appropriate binary character representation of the decimal number. my code: public class lab16{public string converttobinary(int input){int a; if(input > 0){a = input % 2; return (converttobinary(input / 2) + "" +a); } return ""; } }