Question

How many different elements does A × B have if A has 3 elements and B has 2 elements?

Answer #1

How many elements does Z/4Z have?

Problem 3: (a) How many elements in S8 commute with the
permutation (123)(45678)? (b) How many elements are there in S8
with order 15?

How many elements of the specified order does the given
permutation group have?
a) order 10 in S6
b) order 10 in S10

1)Let the Universal Set, S, have 97 elements. A and B are
subsets of S. Set A contains 45 elements and Set B contains 18
elements. If Sets A and B have 1 elements in common, how many
elements are in A but not in B?
2)Let the Universal Set, S, have 178 elements. A and B are
subsets of S. Set A contains 72 elements and Set B contains 95
elements. If Sets A and B have 39 elements...

How many subgroups of order 3 does D3 have?

3. Consider the SF4 molecule.
b) How many stretching vibrations does the molecule have, and what
are their symmetries? Which ones appear in an IR spectrum? Which
ones appear in a Raman spectrum? Sketch the stretching modes.
c) How many bending vibrations does the molecule have, and what are
their symmetries? Which ones appear in an IR spectrum? Which ones
appear in a Raman spectrum?
Dont forget to sketch the stretching nodes

Suppose that the set S has n elements and discuss the
number of subsets of various sizes.
(a) How many subsets of size 0 does S have?
(b) How many subsets of size 1 does S have?
(c) How many subsets of size 2 does S have?
(d) How many subsets of size n does S have?
(e) Clearly the total number of subsets of S must equal the sum of
the number of subsets of size 0, of size...

Circular Permutations and Permutations with Similar Elements
1) In how many ways can three people be made to sit at a round
table?
2) In how many ways can three couples be seated at a round
table, so that men and women sit alternately?
3) In how many ways can five keys be put on a key ring?
4) Find the number of different permutations of the letters of
the word MATHEMATICS.
5) How many different ways can three pennies,...

How many subspaces does R1 have? How many subspaces does R2
have?

discrete mathematics
1. How many element are in A1 È A2 if there are 12 elements A1,
18 elements in A2 and
a) A1 Ç A2 =Æ?
b) | A1 Ç A2 | =1?
c) | A1 Ç A2 | =6?
d) A1 Í A2?
2. There are 345 students at a college who have taken a course
in calculus, 212 who have taken a course in discrete mathematics
and 188 who have taken courses in both calculus and discrete...

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