Determine whether each of these statements is true or false.a) x ? {x}________________b) {x} ? {x}________________c) {x}?{x}________________d) {x)?{{x}} ________________e) ? ? {x} ________________f) ? ? {x}

Solution:Step-1:In this problem we need to determine whether each of the given statements is true or false.a)Let us consider , A= {x}.means x is an element of the set A. Therefore, the given statement is true.Step-2:b)We know that, every set is a subset of itself.That is,.Therefore, the given statement is true. Step-3:c)Let us consider , A= {x}.We know that , means x is an element of the set A , and every set is a subset of itself.So, by using the above conditions is false.Therefore, the given statement is false.Step-4:d)Let us consider , A= {{x}}.means {x} is an element of the set A. Therefore, the given statement is true.Step-5:e)We know that , the empty set is a subset of every set.That is , .Therefore , the given statement is true.Step-6:f)Let us consider , A= {x}.means x is an element of the set A. So, is not an element in {x}.Therefore, the given statement is false.