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Determine whether f : Z × Z → Z is onto if f(m,n)= m-n
Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply
a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)
How many positive integers less than 100 is not a factor of 2,3 and 5?
) How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other?
As for those three guys, John, Bill and Bob, I will only vote for one. Translate into proposition logic.
1. The following formulas have been abbreviated based on the common abbreviation rules. Follow the steps below and translate the formulas into good English.
· Step 1: Re-add the omitted brackets.
· Step 2: If necessary, convert them into some other logically equivalent formula
so as to make it more readable. Write out the rule(s) you use for conversion.
· Step 3: Translate the formulas into `good' English. Try to make your translation as brief/understandable as possible. (For instance, `John and Bill are coming' is better than `John is coming and Bill is coming.')
p: John wants to come to the class.
q: John will come to the class today.
r: John audits the class.
s: John is enrolled in the class.
Hint:
`No matter whether John is going or not, I'm going.' is the translation for (j à i) ^ (⌐j à i),
in which j = John is going, i = I'm going.)
Consider two sets A and B such that A ⊆ B. Find the possible values of x if A = {2, 4, 6, x} and B = {2, 3, 5, 6, x+1}. Ans: x = 3. Please explain.
Consider a relation R= {(1, 1) (1, 3), (2, 2), (2,3) (3,1)on the set A = (1,2,3) Find transitive using warshalls algorithm... closure of the relation R consider
Consider a relation R= {(1, 1) (1, 3), (2, 2), (2,3) (3,123 on the set A = {1,2,37 Find transitive using warshalls algorithm... closure of the relation R consider
For each of the following pairs of functions, determine whether 𝒇(𝒏) = 𝑶(𝒈(𝒏)) or
𝒈(𝒏) = 𝑶(𝒇(𝒏)).
a. 𝑓(𝑛) = 𝑛(𝑛 − 1)⁄2 and 𝑔(𝑛) = 6𝑛
b. 𝑓(𝑛) = 𝑛 + 2√𝑛 and 𝑔(𝑛) = 𝑛^2
c. 𝑓(𝑛) = 𝑛 + log 𝑛 and 𝑔(𝑛) = 𝑛√𝑛
d. 𝑓(𝑛) = 𝑛 log 𝑛 and 𝑔(𝑛) = 𝑛√𝑛/2
e. 𝑓(𝑛) = 2(log 𝑛)^2
and 𝑔(𝑛) = log 𝑛 + 1
