For each statement, identify and write out the hypothesis and the conclusion. yo
ID: 1946848 • Letter: F
Question
For each statement, identify and write out the hypothesis and the conclusion. you may have to introduce your own variable(s) to do it:a) 2^n > n for all natural numbers n.
b) The reciprocal of every rational number is rational.
c) The sum of two odd integers is even.
d) Any natural number whose digits add up to something divisible by three is itself divisible by three.
e) Suppose f is a continuous function and A is a compact set. Then f(A) is also compact.
f) Any two real numbers have a rational number between them.
Explanation / Answer
a)
Hypothesis: For all n in the set of natural numbers
Conclusion: 2^n > n
b)
Hypothesis: For every rational number r
Conclusion: 1/r is a rational number
c)
Hypothesis: For two odd integers m and n
Conclusion: n+m = 2k (an even integer)
d)
Hypothesis: For a natural number n whose digits add up to x where 3|x (3 divides x)
Conclusion: 3|n (n is also divisible by 3
e)
Hypothesis: If f is a continuous function and A is a compact set
Conclusion: then f(A) is also compact
f)
Hypothesis: For any two real numbers x,z
Conclusion: there exists a rational number y so that x<y>z
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