Review materials for "Discrete Mathematics"

Class_______________________________ Name_____________________ Score______________________

1. Multiple choice questions (choose a correct answer for each question, 2 points per question, 2 points in total, 20 points)

1. In the following sentences, it is a proposition.

a. It's sunny today b. It's too hot today! c. Do you feel good today? d. Go climbing the mountain today?

d.pqr

3. Suppose p: All of my class are boys, then p can be repeated as.

a. All my class are not boys b. There are no girls in my class c. There are not all boys in my class d. There are no boys in my class

4. Among the following formulas, it is the Yongzhen formula.

a.p→(pvq)?b.p→(p∧q)?c.(p→q)∧p?d.(p→q)∧q

7. Suppose the set a={1,2,3,4},b={2,4,6}, then ab=.

a.{1,3}b.{1,2,3,4,6}c.{2,4}d.{1,3,6}

8. Suppose the set a={1,2,3}, which is less than the relationship r={

|x,yax

a.{<2,1>,<3,1>,<3,2>}b.{<1,2>,<1,3>,<2,3>}

c.{<2,1>,<3,2>}d.{<1,2>,<2,3>}

9. In the equivalent meaning of a formula, which of the following is unique?

a. Disjunction paradigm b. Combination paradigm c. Main disjunction paradigm d. None of the above answers are correct

10. Suppose the relationship r={,,,,

,

}, then r has the nature of relationship.

a. Reflexive b. Symmetry c. Transmission d. Reverse Reflexive self-reflective

2. Fill in the blanks (3 points for each blank, 30 points in total)

1. Suppose the set a={1,2,3,4},b={2,4}, then b-a=__________________.

2. If the relationship r is reflexive, if and only if the element ______________________ on the main diagonal in the relationship matrix; if the relationship only has symmetry, if and only if the relationship matrix is ​​______________.

3. When the proposition formula a=p→(q∧r), then a has a total of _____ different assignments; where the assignment (0,1,0) makes the true value of a __________.

4. Suppose the set a={a,b,c},b={1,2}, then axb=__________________.

3. Judgment questions (judgment the true (t) and false (f) value of the conclusion, 2 points per question, 2 points in total)

1. If avc<=>avb, then b<=>c.

2. If a∧c<=>a∧b, then b<=>c.

5.x∈{x,y}-{{x},y}.

6.{1,5} belongs to or equal to {1,{1,5},5}.

7. If anb=a, then b=e.

8. If aub=a, then b=empty set.

9. Suppose a={a,b,c,d}, then {{a},{a,b,c},{d}} is a division of a.

10.s(r)=rur-1.

4. Calculation questions (10 points per question, 30 points in total)

1. Find the main dissection paradigm of (p→q)r.

2. Proof: (a-b)n(a-c)=a-(buc).

3. Suppose the relationship r on set a={a,b,c},a={,,,

,

},

1) Draw the relationship diagram of r;

2) Write out the relationship matrix of r;

3) Ask what properties of relationships r have (self-reflexive, symmetry, transmission, anti-reflexive, anti-symmetrical);

4) Write out the symmetric package s(r) using the listing method;

- Digital circuit -

Fill in the blanks: 2 points per question

1. Expand the following binary numbers (see corner mark) according to the corresponding weight position:

(826)10=

(96.38)10=

(10101)2=

(101.11)2=

2, (75.5)10 is converted to binary number as

(11011)2 is converted to a decimal number

3. Use the inversion law (i.e., DeMorgan's law) to transform the following formula:

___

a+b=

___

a*b=

4. Write out the characteristic equation of the jk trigger:

q^(n+1)=

5. The waveform of the output signal of the multi-oster is

6. The two states of monostable triggers working are? and?

8. To design a meth-digit counter, the minimum number of triggers required is:

9. In digital circuits, the three most basic logical operations are

10. List three common combination logic circuits

List two common timing logic circuits
Chapter completed!