Applying What You’ve Learned Use the following table of student information to determine whether the statements in Exercises 35 − 40 are true or false. If a statement is false, explain why it is false using rules of quantifiers that we have developed. For example, the statement “All sophomores are on scholarship” is false because “There exists a sophomore (Stephen) who is not on scholarship.” Name Year Scholarship Athlete Commuter Lennox Freshman Yes Yes No Marilu Freshman No No Yes Stephen Sophomore No Yes Yes Omarosa Junior Yes No No Tito Sophomore Yes Yes Yes Nadia Sophomore Yes Yes No Piers Junior Yes No Yes All sophomores are commuters.
Applying What You’ve Learned Use the following table of student information to determine whether the statements in Exercises 35 − 40 are true or false. If a statement is false, explain why it is false using rules of quantifiers that we have developed. For example, the statement “All sophomores are on scholarship” is false because “There exists a sophomore (Stephen) who is not on scholarship.” Name Year Scholarship Athlete Commuter Lennox Freshman Yes Yes No Marilu Freshman No No Yes Stephen Sophomore No Yes Yes Omarosa Junior Yes No No Tito Sophomore Yes Yes Yes Nadia Sophomore Yes Yes No Piers Junior Yes No Yes All sophomores are commuters.
Solution Summary: The author analyzes whether the statement "All sophomores are commuters" is true or false using the given table.
Use the following table of student information to determine whether the statements in Exercises
35
−
40
are true or false. If a statement is false, explain why it is false using rules of quantifiers that we have developed. For example, the statement “All sophomores are on scholarship” is false because “There exists a sophomore (Stephen) who is not on scholarship.”
Why researchers are interested in describing measures of the center and measures of variation of a data set?
Let Χ be a real-valued character (mod k). Let
k
S = Σnx(n).
n=1
If (a, k) = 1,
ax(a)S = S (mod k).
(iii) Write k = 2ºq where q is odd. Show that there is an integer a
with (a, k) = 1 such that a = 3 (mod 2ª) and a = 2 (mod q).
Deduce that 12S = 0 (mod k).
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