if and only if discrete math
if and wish exercises
Ngày tải lên :
29/09/2013, 01:10
... chỉ
điều kiện.
Ex: If I were to ask him nicely, he would help
4- WISH :
a- Ước ở hiện tại:
S + Wish + S + V.ed +
(If only) were
could + V
Ex: I wish I were on the beach now.
If only I were on ... wet if you (wear) a raincoat.
15- If they (know) your address, they would visit you
16- If it rains tomorrow, we (not go) on a picnic.
17- She would pass the exam if she (study) harder.
18- If ... would Lan do if she ………… the Miss world.
a. would be b. were c. will be d. is.
24- If I were in your place, I …… ….a trip to England.
a. will make b. had made c. made. d. would make.
25- If I …………...
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If I do … and If I did… & If I knew… I wish I new
Ngày tải lên :
27/10/2013, 22:15
... huống như vậy, bạn dùng cấu trúc if+ thì quá khứ (if I knew /if you
were /if we didn’t…) nhưng nghĩa của câu là hiện tại không phải quá khứ.
Tom would read more if he had more time. (but he doesn’t ... be able to go out)
If I were you, I wouldn’t buy that coat hoặc If I was you…
Nếu tôi là anh tôi sẽ không mua cái áo khoác đó.
I’d go out if it weren’t raining hoặc if it wasn’t raining…
... dùng would ở mệnh đề if:
I’d be very frightened if somebody pointed a gun at me. (không nói if somebody would point”)
Tôi sẽ rất sợ nếu có ai đó chĩa súng vào tôi.
If I didn’t go to their...
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Tài liệu Prolog Experiments in Discrete Mathematics, Logic, and Computability pdf
Ngày tải lên :
21/02/2014, 09:20
...
commercial and public versions. The language is easy to learn and use
because its syntax and semantics are similar to that of mathematics and
logic. So the learning curve is steep and no prior ... assumption that X stands
for b. This is an example of “unification” and it is a basic ingredient in the
matching process used for computation in logic programming.
Unification
Unification is the ... block
b if they are both on top. To accomplish this we’ll need to test whether
the two blocks are on top and, if so, to retract one clause and to assert
another clause. We’ll modify the program...
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Wacky word problems games and activities that make math easy and fun
Ngày tải lên :
16/02/2014, 22:51
... Lynette.
Wacky word problems : games and activities that make math easy and fun / Lynette Long.
p. cm. —(Magical math)
Includes index.
ISBN 0-471-21061-7 (pbk. : alk. paper)
1. Mathematical recreations. ... 10/25/04 10:07 AM Page 31
WACKY W ORD
P ROBLEMS
Games and Activities
That Make Math Easy and Fun
Lynette Long
John Wiley & Sons, Inc.
Magical Math
ffirs.qxd 10/25/04 9:55 AM Page iii
15
III
M ... 10/25/04 10:07 AM Page 22
WACKY W ORD
P ROBLEMS
Games and Activities
That Make Math Easy and Fun
Lynette Long
John Wiley & Sons, Inc.
Magical Math
ffirs.qxd 10/25/04 9:55 AM Page iii
2
For example,...
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Tài liệu MATHLETICS How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football docx
Ngày tải lên :
21/02/2014, 06:20
... side) of length
c and two other sides of lengths a and b. Recall from high school geometry
that the Pythagorean Theorem states that a triangle is a right triangle if and
only if a
2
ϩ b
2
ϭ c
2
. ... Excel contains
a function RAND(). If you type ϭ RAND() in any cell and hit the F9
key, the number in the cell will change. The RAND() function yields any
number between 0 and 1 with equal probability. ... Wayne L.
Mathletics : how gamblers, managers, and sports enthusiasts use
mathematics in baseball, basketball, and football / Wayne Winston.
p. cm.
Includes bibliographical references and index.
ISBN...
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Tài liệu Discrete Math for Computer Science Students doc
Ngày tải lên :
21/02/2014, 09:20
... S
2
∪ S
3
and S
2
and S
3
are disjoint, and so, by the sum principle,
Equation 1.7 must hold.
We now give a proof for general n and k.
Theorem 1.3 If n and k are integers with n>0 and 0 <k<n, ... D precede C and E. Since there are 3! ways to arrange A,
B, and D, and 2! ways to arrange C and E,bythe product principal, there are 3!2! = 12 lists in
which A, B, and D precede C and E.Foreach ... as defined in the
footnote).
cParts b and c of this problem prove that a relationship is an equivalence relation if
and only if it is symmetric, reflexive, and transitive. Explain why. (A short...
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DISCRETE MATHEMATICS NOTES pot
Ngày tải lên :
08/03/2014, 12:20
... integers.
➊ If a|b then a|kb for any k ∈Z.
➋ If a|b and b|a, then a = ±b.
➌ If a|b and b|c then a|c.
➍ If c divides a and b then c divides any linear combination of a and b. That is, if a,b,c,m,n ... X[n−i−1].
This holds as long as i < n−i −1, that is 2i < n−1, which happens if and only if 2i ≤ n−2, which happens if and only if
i ≤(n−2)/2. We now use a swapping algorithm, say the one of example ... triangle if and only they satisfy the triangle inequalities::
a+ b > c,
b+ c > a,
c+ a > b.
✎
✍
☞
✌
Algorithm 3.1.1: ISITATRIANGLE((a,b,c))
if ((a > 0) and (b > 0) and (c > 0)
and...
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Determinants and their applications in mathematical physics vein r , dale p
Ngày tải lên :
17/03/2014, 14:29
... rejecter and retainer minors, their simple and scaled
cofactors, their row and column vectors, and their derivatives have all been
expressed in a notation which we believe is simple and clear and ... proved by both a Grassmann and a
classical method in Chapter 3 after the definitions of second and higher
rejector and retainor minors and cofactors.
3.1 Cyclic Dislocations and Generalizations 17
Hence
n
j=1
C
1
C
2
···C
∗
j
··· ... al-
phabetical order and reference to Mathematical Reviews, Zentralblatt făur
Mathematik, and Physics Abstracts have been included to enable the reader
who has no easy access to journals and books to...
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Just and Only pot
Ngày tải lên :
19/03/2014, 22:20
...
Just and Only
Ví dụ:
Nếu nói “He was just here”, có nghĩa là nói “Anh ta vừa mới vừa ở đây vài phút
trước thôi”/ "Anh ta vừa mới ở đây mà".
Cơ bản là mỗi khi sử dụng only , ... cả. Nó làm cho câu nói của chúng ta nghe có vẻ lịch sự và nhẹ
nhàng hơn.
Câu thứ hai dùng only có nghĩa là tôi muốn cám ơn nhưng lại không muốn nói
gì nữa sau đó.
Nhiều trường hợp, ... lệnh hơn nhỉ?]
Có những trường hợp chúng ta có thể sử dụng “just” nhưng không thể thay thế
bằng only .
...
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discrete mathematics
Ngày tải lên :
27/03/2014, 11:56
... Cucumbers are green and not seedy,
Answer: In this case, 1, 2, and 3 all negate the statement cucumbers are green AND
seedy.
c. 2 < 7 and 3 is odd.
1. 2 > 7 and 3 is even.
2. 2 ≥ 7 and 3 is even.
3. ... and it is not 3.
Answer: In this particular situation there are two forms which negate the statement
above. They are: 1 and 3.
b. Cucumbers are green and seedy.
1. Cucumbers are not green and ... reduced.
A → B
b. Tax rates will be reduced only if Anita wins the election and the economy
remains strong.
Answer:
A: Tax rates will be reduced.
17.Verify each with a truth table:
d. A → A \/...
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Discrete Mathematics ppt
Ngày tải lên :
31/03/2014, 12:20
... graphs.
Theorem 10.1 (a) A graph G is a tree if and only if it is connected, but deleting any of
its edges results in a disconnected graph.
(b) A graph G is a tree if and only if it contains no cycles, but ... factorizations. (Indeed, if
necessary, we can interchange the left hand side and the right hand side so that the smallest
prime in any of the two factorizations occurs on the left hand side; and then change ... ?
n −1
2
.
So if k < (n−1)/2, then
n
k
<
n
k + 1
; if k = (n−1)/2, then
n
k
=
n
k + 1
(this is the
case of the two entries in the middle if n is odd); and if k > (n−1)/2,...
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Lecture Notes on Discrete Mathematics doc
Ngày tải lên :
31/03/2014, 12:20
... G.
1. Ha = H if and only if a ∈ H,
2. Ha is a subgroup of G if and only if a ∈ H,
3. either Ha = Hb or Ha ∩Hb = ∅,
4. Ha = Hb if and only if ab
−1
∈ H.
Furthermore, aH = Ha if and only if H = aHa
−1
= ... left cosets of H in G:
1. aH = H if and only if a ∈ H,
2. aH is a subgroup of G if and only if a ∈ H,
3. either aH = bH or aH ∩ bH = ∅,
4. aH = bH if and only if a
−1
b ∈ H.
Similarly one obtains ... 3 A’s
and 6 B’s? What if we are interested in the strings that are formed using +’s and 1’s in
place of A’a and B’s?
Solution: Note that the 3 A’s are indistinguishable among themselves and the...
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