se an element argument to prove the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B, if A ⊆ B then  Bc ⊆ Ac. Some of the sentences in the following scrambled list can be used to write a proof. Suppose A and B are sets and A ⊆ B. Let x ∈ B. Hence, x ∉ A, because of the definition of subset and that A ⊆ B. Therefore, by definition of complement x ∈ Ac, and thus, by definition of subset, Bc ⊆ Ac. Suppose A and B are sets and A ⊆ B. Let x ∈ Bc. Hence, x ∉ A, because A ∩ B = ∅. By definition of complement, x ∉ B. Proof: We construct a proof by selecting appropriate sentences from the list and putting them in the correct order.

Solve the following differential equation: yde+xdy 1-x²y² +ædr=0. = constant.

Give formal well-written proofs when you are proving a result or a counter example otherwise Prove or disprove each of the following statements. For all sets A and B, if A n B = B, then B subset A.

Consider the following statement. If U denotes a universal set, then UC = 0. Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Use the element method for proving that a set equals the empty set. Let U be a universal set and suppose UC + Ø. So, by definition of complement x EU. Thus x EU and x € U, which is a contradiction. Then there exists an element x in UC. But, by definition of a universal set, U contains all elements under discussion, and so x E U. Let U be a universal set and suppose UC - 0. So, by definition of complement x ¢ U. But, by definition of a universal set, UC contains no elements. Proof by contradiction: Select-- 2 Select- Select 4. --Select- 5. -Select 6. Hence the supposition is false, and so UC = 0. Need Help? Read It