Finite and Infinite Set

Q. List the set of letters of the following words in Roster form.

(i) INDIA
(ii) PARALLELOGRAM
(iii) MISSISSIPPI

Q.

Classify the set of multiples of $2$ as finite or infinite set.

Q. how to prove that there are infinite prime numbers?

Q.

Classify the set of multiples of $5$ as empty, finite or infinite set.

Q. If $\text{A}=\{x:x\text{is a prime number and}x<13\}$, then find the number of proper subsets of set $\text{A}$.​

1. $32$
2. $64$
3. $31$
4. $63$

Q. Let Z be the set of all integers and A = {(x, y); x4y4 = 175, x, y E Z} B = {(x, y); xy, x, y EZ} Then, the number of elements in An B is

Q.

State whether each of the following statements is true or false. If the statement is false, rewrite the given statement correctly:

If $\mathrm{P}=\{\mathrm{m},\mathrm{n}\}$ and $\mathrm{Q}=\{\mathrm{n},\mathrm{m}\}$ then $\mathrm{P}\times \mathrm{Q}=\left\{\right(\mathrm{m},\mathrm{n}),(\mathrm{n},\mathrm{m}\left)\right\}$

Q. Every mapping is a relation but every relation is not a mapping.

1. True
2. False

Q. The set of positive integers greater than 100 is a finite set.

1. False
2. True

Q.

Classify the set of multiples of $3$ more than $4$ and less than $5$ as empty or singleton set.

Q. All the factors of 12 forms a finite set.

1. False
2. True

Q. Write one rational & one fractional number between 0.515115111…. and 0.535335333……