Prove that for all sets a and b, if p(a) ⊆ p(b), then a ⊆ b (we can take generic sets a and b, assume p(a) ⊆ p(b), and prove a ⊆ b. what is the typical technique to prove a set is a subset of another

recall that the power set of a set a, denoted , is the set of all subsets of a. the subset includes the set a itself.

assume that for some generic sets a and b. symbolically, means that (for all elements x from the universe, if x belongs to set , then x belongs to set ). now we have to show that .

since a is a subset of a, . since we assumed that is true, it follows from that . by definition of power set, .

the typical technique to prove a set is a subset of another is true is to use a direct proof. the statement means that, for all elements x from the universe, implies that . thus we do a direct proof by

after we have made the inference, since we showed that is true for any arbitrary, generic value x from the universe, the rule of universal generalization can be invoked to generalize that x is a subset of y.

1. -16 Radical(5i)

2. -10 Radical(5i)

3. -8 Radical(5i)

4. -4 Radical(5i)

Hope this helps :)