Given nonempty sets a and b, prove that every set in p(b − a) ⊆ p(b) − p(a).

Proof:

Let . As we chose in we know that . Since by transitivity we get:

.

If is the empty set, we already have that . But if is not empty, that means that it can't be subset of , because is already  subset of , and those sets do not share any element. In other words:

As can't be subset of , then . was an arbitrary element, and

Thus, , where we conclude that

yes

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step-by-step explanation:

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9