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- Label each of the following statements as either true or false. Every upper bound of a nonempty set S must be an element of S.15. Let be a binary operation on the non empty set . Prove that if contains an identity element with respect to , the identity element is unique.Label each of the following statements as either true or false. 2. for all nonempty sets A and B.
- Label each of the following statements as either true or false. Let ={a,b,c}. The power set P(A) is closed with respect to the binary operation of forming intersections.Let R be the relation defined on the set of integers by aRb if and only if ab. Prove or disprove that R is an equivalence relation.(See Exercise 26) Let A be an infinite set, and let H be the set of all fS(A) such that f(x)=x for all but a finite number of elements x of A. Prove that H is a subgroup of S(A).