# Discrete Mathematics | Week 5

## Quiz

1. Which of the following is(are) true for the given function?
f: R โ R
f(x)=x2+
2 where, R is a set of real number

a. ๐ is not injective

d.  ๐ is not surjective

Explanation

2. Consider the following table:

We can think of this as a function ๐ from the set of students to the set of integers between 160 and 170. Now pick out the correct statement from the following.

ย d.ย ๐ is neither one to one nor onto

Explanation

3. Let ๐: ๐โ๐ such that f(x)=x/2+7

b. ๐ is bijective

Explanation

4. If a function is defined as ๐(๐ฅ)=2๐ฅ+15 then the value of f-1(25) is

b. 5

Explanation

5. Set ๐ถ has cardinality ๐ and a total of 5040 bijective functions. What is the value of ๐2?

d. 49

Explanation

6. find the domain and range of the following real-valued function. f(x)=โ(3โx)

d. domain= {๐ฅ โ R | ๐ฅ โค 3}
range=
{๐ฅ โ R | ๐ฅ โฅ 0}

Explanation

7. If ๐ and ๐ are function from ๐ to ๐ and ๐(๐ฅ)=3๐ฅ2+๐ฅโ13 and ๐(๐ฅ)=20/(3๐ฅ+8) then ๐o๐ (12) is.

c. โ1443/121

Explanation

8. Let us define a function ๐: ZโZ as follows,
f(x)= {x/2 if x is even, 0 if x is odd
Z is a set of integers.

a. onto but not one-to-one

Explanation

9. The relation ๐ is defined as ๐ = {(x, y): ๐ฅ, y โ N, ๐ฅ + y = 5} then the range is?

d. {1,2,3,4}

Explanation

10. Let ๐ด be set with cardinality ๐ and set ๐ต with cardinality ๐, there are a total of 3024 one to one function from ๐ด to ๐ต, what are the values of ๐ and ๐ respectively?

b. 4 and 9

Explanation

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