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Out of a group of ten residents in a certain county, 3 are Republicans, 5 are
Democrats, and 2 are Independents. How many unique partitions of this group
of residents are there by political party?
38) You have eight distinct pieces of food. You want to choose three for breakfast,
two for lunch, and three for dinner. How many ways to do that?
39) You teach a class with 90 students. In a rather severe effort to combat grade
inflation, your department chair insists that you assign the students exactly 10
A’s, 20 B’s, 30 C’s, 20 D’s, and 10 F’s. How many ways to do this?
40) How many 13-card bridge hands have 4 of one suit, 3 of one suit, 5 of one suit, 1
of one suit?
multiple-choice test contains 10 questions. There are four possible answers for each question. a) In how many ways can a student answer the questions on the test if the student answers every question? b) In how many ways can a student answer the questions on the test if the student can leave answers blank?
Show using the rules of resolution/inference, that no
single assignment of truth values to p, q, r makes all
the disjunctions p V-9, p V-9,9 V r,
qVT, V revaluate to true. Proof using truth
na
[T] Find "\\mathbb{Q}\\cup \\mathbb{N}" ?
R= {(1,3) ,(1,4) , (3,2) , (3,3), (3,4)} on A={1,2,3,4}
write a logical conclusion of the following sets of statements (1)if david gets an A in math class, he will receive money from his parents (2)if david receives money from his parents he will save it up (3)if david saves his money, he will use ut to buy a new PlayStation (4) david git an A in math class
List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a, b) ∈ R if and only if a | b.
Let R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}
R={(1,2),(1,4),(2,1),(2,4),(3,2),(3,4)}
is a relation on set A={1,2,3,4}
A={1,2,3,4}
Suppose a Rn b
means that there is a path of length n from a
to b
Which of the elements are R3?
LetR={(1,2),(2,1),(2,3),(2,4),(4,1),(4,3)}
R={(1,2),(2,1),(2,3),(2,4),(4,1),(4,3)}
is a relation on
setA={1,2,3,4}
Suppose aRnb
means that there is a path of length n
from a to b
Which of elements are of
R∞
Let A, B, C, D denote, respectively, art, biology, chemistry, and drama courses.
Find the number N of students in a dormitory given the data:
12 take A, 5 takeAand B, 4 takeB and D, 2 take B, C,D,
20 take B, 7 takeAand C, 3 takeC and D, 3 take A, C,D,
20 take C, 4 takeAand D, 3 take A, B,C, 2 take all four,
8 take D, 16 takeB and C, 2 take A, B, D, 71 take none.
#340153 on Dec 2023