Discrete Mathematics Answers

Prove the following : (a) If |A1| = n1, |A2|= n2 and |A3|= n3 then |A1 x A2 x A3| = n1n2n3

ind the number of integer solutions to the equation x1+x2+x3=40 where, 6<=x1>=15, 5<=x2>=20 and 10<=x3>=25

Use truth table to test the validity of:
If I study, then I will not fail mathematics
if I don't play basketball, then I will study
But I failed mathematics
Therefore I must have played basketball

1. For a sequence 128, 64, 32, ……………………….. what is the value 12th term of this sequence?

2.The 3rd and 7th term of a G.P. are 81 and16 respectively, find the 1st and 5th term

3.A student is to answer all the nine questions in an examination. It is believed that the sequence in which the questions are answered may have a considerable effect on the performance of the student. In how many different order can the question be answered

4.A bus starts with 6 people and stops at 10 different stops. how many different ways can the 6 people depart if any passenger can depart at any bus stop

5. how many 3 digits numbers greater than 300 can be formed using the digits 1, 2, 3, 4, 5 if no digit can be repeated and the first digit cannot be 3?

6.In how many way can 6 people take place at a round table?

Example of a subset of a set that's contains 4element

Find the sum of product expansion of the Boolean Function given by F(x,y,z)=x.(y+z') by using identities and also by using table

If A and B are the set of even integers and set of odd integers, respectively, find( A union B) and (A union B) ^c

Let $a_n\geq \frac{2^n-1}{n}$ and let $\nu\leq \lfloor{\log_2 n}\rfloor$. Show that $a_n-\nu> 0$.

State whether the following statements are true or false. Give reasons for your answer.
i) The rule given below is a function
f :{2, 3}®{4, 7}: f (2) = 4, f (2) = 7, f (3) = 7
ii) For two non-negative integers r and n s.t., r £ n
r
n
r
n
r
n C C C 1
1
+
−
+ =
iii) The normal curve for
= −¥ < < ¥
−
f e x
x
;
2
1 2
2
1
p
attains its maximum at x = 0 .
iv) The magnitude of a vector product u×v is equal to the area of a triangle having u and v as
two of its sides.
v) If X has the uniform distribution on [a, b] , then mean of X is
2
b − a
.