8.(a) Give a direct proof that when w, x are real numbers such that w|sx|, we have \w + x] 2 (b) s |x| Recall that a subset TCS of a countable set S will also be countable. Use proof by contradiction to show that a superset W2V of an uncountable set V must also be uncountable.

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8.(a) Give a direct proof that when w, x are real numbers such that |w|s|x], we have
\w + x|
2
(b)
s |x|
Recall that a subset TCS of a countable set S will also be countable.
Use proof by contradiction to show that a superset W2V of an uncountable set V must
also be uncountable.
Transcribed Image Text:8.(a) Give a direct proof that when w, x are real numbers such that |w|s|x], we have \w + x| 2 (b) s |x| Recall that a subset TCS of a countable set S will also be countable. Use proof by contradiction to show that a superset W2V of an uncountable set V must also be uncountable.
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