Mathematical logic problem Sets (1)

From now on, we will do some training in mathematical logic. One of the skills a programmer must have.

A,b of any event () is established
A. P (a∪b) =p (a) +p (B)
B. P (b-a) =p (b)-P (A)
C. P (a∪b) =p (A) +p (B)-P (A∩B)
D. P (A∩B) =p (A) p (B)
Reference Answer: C
Analytic: The most basic probability theory, does not explain.

Some rabbits have been raised. He was asked how many female rabbits he had. How many male rabbits. He replied that of the rabbits he had raised, each male had one less female companion than its male companion, while a female male companion was twice times less than its female companion two.
According to the above answer, you can tell how many female rabbits it has raised. How many male rabbits. （ ）
A. 8 male rabbits, 6 female rabbits.
B. 10 male rabbits, 8 female rabbits.
C. 12 male rabbits, 10 female rabbits.
D. 14 male rabbits, 8 female rabbits.
Reference Answer: A
Analysis: Must see the topic clearly, (did not read the topic of my face, but also try to use the two-point diagram ...) In fact, it is very simple to set the female as Y and the male as X. Then X=y-1-1 and y= (x-1) *2-2, the solution y=8,x=6.

For the first time a ship sailed 21-kilometer and 4-kilometer, the next day in the same river downstream of 12-kilometer, upstream of 7-kilometer, the results two times the time spent is equal. The ratio of the speed of the ship to the current ship speed is () if the ship's velocity and velocity remain unchanged.
A. 2:1
B. 3:1
C. 3.5:1
D. 4:1
Reference Answer: B
Resolution: Set the ship itself at a speed of x km/h, flow speed of y km/h, then the speed of the boat (x+y) km/h, the current boat speed (x-y) km/h. According to the need to be available; 21/(x+y) +4/(x-y) =12/(x+y) +7/(x-y), from which ( X+y)/(x-y) = 3, that is, the speed of the boat is 3 times times the speed of the upstream ship.

500 dominoes neatly lined up, numbered 1, 2, 3 、......、 499, 500 in order. For the first time take away all the odd positions of the dominoes, the second time from the remaining dominoes away from the odd position of the dominoes, and so on. Can you tell me the number of the last dominoes left?
A. 128
B. 250
C. 256
D. 500
Reference Answer: C
Resolution: There are 250 even numbers left after the first time: 2,4,6,8 ... 498,500 (a multiple of 2 left, 2 of the First Party)
There are 125 even numbers left after the second: 4,8,12,16 ... 496,500 (multiples of 4 left, 2 of two times)
After the third time there are 62 even: 8,16,24....488,496 (multiples of 8 left, 2 of three)
..........................................................................
After the eighth time left 1 even: 256 (2 of the eight-square multiple left)

The 1-meter-long square is a total of 2,100, piled into a solid cuboid, its height is 10 meters, long, wider than high, ask the cuboid length and width and is how many meters.
A. 41
B. 31
C. 37
D. 29
Reference Answer: D
Parsing: Integer programming issues. High is 10 meters, then long times wide =2100/10=210 will 210 decomposition decomposition, get 210=2∗3∗5∗7, here, because the length and width are greater than 10, so can only take 2∗7 and 3∗5 so long 15, width of 14.

A, B and C, one is Fujian people, one is Hebei, one is Hunan people. Now only know: C than the age of Hunan, a and Hebei people are not the same age, Hebei people younger than B. This can be introduced:
A. Not A Hunan man
B. People in Hebei province are younger than their armour
C. People in Hebei are older than Fujian people
D. Hunan people of the youngest age
Reference Answer: D
Analysis: By the condition that A and B are not Hebei people, so C is the Hebei people
C than Hunan People's Congress, and b than Hebei (c) Large, so B can only be Fujian people, a Hunan people
So age a < C < b, Hunan people < Hebei people < Fujian people

Xiao Zhao and the penny two people from the dormitory and the library at the same time starting, opposite and line. After a period of time, two people met halfway through, Xiao Zhao continue to advance to the library, at this time: if the money continues to the bedroom forward, then when the small Zhao arrived at the library, the money from the bedroom there are 600 meters, if the money immediately turn to the library forward, then when the small Zhao arrived at the library is, a penny away from the library is Then the distance between the library and the dormitory is __.
A. 1300m
B. 1250m
C. 800m
D. 1050m
E. 1100m
F. 900m
Reference Answer: F
Analytical:
Premise: ⒈ has 5 5 colors of the house; ⒉ the owner of each house is different; ⒊ 5 each person drinks only one beverage, smokes a brand of cigarettes, raises a pet; 4. No one has the same pet, smokes the same brand of cigarettes, drinks the same drink.
Tips:
*⒈ the British live in a red house;
*⒉ a Swede to raise a dog;
*⒊ the Danes for tea;
*⒋ Green House on the left of the White House;
*⒌ Green house owner drink coffee;
*⒍ Smoke Pall Mall people to raise birds;
*⒎ Yellow house owner smoked Dunhill Smoke;
*⒏ who live in the middle house drink milk;
*⒐ The Norwegian people live in the first house;
*⒑ Smoke mixed cigarette people live next to the cat;
*⒒ raise horse people live in smoke Dunhill next to people;
*12. A man who smokes blue master smokes a beer;
*⒔ Germans smoked drince smoke;
*⒕ Norwegian people live next to the Blue House;
*⒖ smoke mixed smoke people neighbors drink mineral water.
Question: Who keeps goldfish?
A. British
B. Swedes
C. Danish People
D. Germans
E. Norwegian people
Reference Answer: D
Analytical:
First, the identified information is generated: The first house is Norwegian, next door is the Blue House, the third in the middle is drinking milk.
1. Then according to the Green house on the left side of the White House (ie adjacent) and the green House people are drinking Starbucks or cat poop or the Pacific Ocean ... , and the third house is for drinking milk, so the fourth house is green, and the fifth House is white; Arrange: _ Blue _ green white; The first and the British live in the Red House can be drawn: yellow, blue, red, green and white; then the yellow house with the people smoking DH, now the information is:

2. Next analysis drink: Now known is a third house the British drink milk, the fourth House green coffee; Then there are three other drinks that are not assigned: Danish tea, BM beer and the neighbour's mineral water that smokes the mixture; by the neighbour mineral water mixed smoke with known information knows, Only the people in the Blue House smoked mixed smoke while the neighbour yellow Norwegian drank mineral water. So the last man in the house smoked bm and drank beer; so the man left an indeterminate blue house was a Dane, drinking tea. Now the information is:

3. The following analysis of nationality: By the Germans, Dr combined with the figure can immediately know that the Germans live in the green house, then the remaining White House live in Sweden.
4. Next is smoke: Smoke left a pit to fill in the British pumping pm;
5. Next is the pet: the Swede raises Wang; the Englishman who smokes the PM raises the bird, the horse man lives beside DH, the Danish raises the horse, the man who smokes the mixed smoke lives next to the cat, but the Englishman does not have a cat, so it is a Norwegian. (Norwegian salmon, Meow Master is very satisfied);
6. All the information here has been used up, all the basic information is also analyzed; Hey, what kind of pet does the Germans keep? Read the questions, OH. To keep goldfish.
A. -2,2
B. 3,-3
C. -3,3
D. 2,-2
Reference Answer: D
Parsing: Assuming the original function is F (x,y), the equation in question is the total differential of F (x,y), note: P DX + Q dy, where P is f (x,y) for x, Q is F (x,y) is biased against Y, and the inverse of the partial derivative is derived from its integral formula F (x,y) =x2y3−y2sinx+y, So p=2xy3−y2cosx,q=3x2y2−2ysinx+1. The formula in the control question can be a=2,b=-2.