Consider the following statements
Q: For all real numbers n, if ?n is rational then ?n is not irrational or n is positive.
R: If Tom is Ann's father then Jim is her uncle and Sue is her aunt or Mary is her cousin.
In English, what are the negations, converses, and contrapositives of Q and R? You do not need to justify the correctness of the statements.
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Consider the following statements Q: For all real numbers n, if ?n is rational then ?n...
(1 point) [4 Marks] Consider the following statements Q : There exists a real number n such that n? > 100 implies n < 10 and n > 0 R: If Tom is Ann's father then Jim is her uncle or Sue is her aunt or Mary is her cousin In English, what are the negations, converses, and contrapositives of Q and R? You do not need to justify the correctness of the statements. A. I am finished this question
Q:Q: There exists a real number nn such that n2>100n2>100 implies n≤10n≤10 and n>0n>0 R:R: If Tom is Ann's father then Jim is her uncle and Sue is her aunt and Mary is her cousin. In English, what are the negations, converses, and contrapositives of QQ and RR? You do not need to justify the correctness of the statements.
Suppose we tried to apply our real analysis definitions/methods to the set of rational numbers Q. In other words, in the definitions, we only consider rational numbers. E.g., [0, 1] now means [0, 1] ∩ Q, etc. In this setting: (a) Find an open cover of [0, 1] that contains no finite subcover. Hint: Fix an irrational number α ∈ [0, 1] (as a subset of the reals now!) and for each (rational) q ∈ [0, 1] look for an...
Suppose we tried to apply our real analysis definitions/methods to the set of rational numbers Q. In other words, in the definitions, we only consider rational numbers. E.g., [0, 1] now means [0, 1] n Q, etc. In this setting: (a) Find an open cover of [0, 1] that contains no finite subcover. Hint: Fix an irrational number a € [0, 1] (as a subset of the reals now!) and for each (rational) qe [0, 1] look for an open...
6 Set Operations • R, the set of real numbers • Q, the set of rational numbers: {a/b: ab € ZAb0} • Z, the set of integers: {..., -2,-1,0,1,2,...} • N, the set of natural numbers: {0,1,2,3,...} (e) What is NUQ? Q? (f) What kind of numbers are in R (g) If SCT, what is S T?
Question 4 of the image Prove that, for all n 1 1 Arrange the following rational numbers in increasing order: (i) x, is a rational number 61/99, 3/5, 17/30, 601/999, 599/1001. g 0 2 Find positive integers r and s such that r/s is equal to the repeating decimal (ii) 2 x5/2. Find an expression for x - 5 involving x,-5, and hence explain (without formal proof) why x, tends to a limit which is not a rational number 0.30024....