Domain and Range of a Relation

Q. Range is the collection of the second elements of all the ordered pairs in a relation.

1. True
2. False

Q.

If $A=\{1,2,3\}andB=\{2,3,4\}$, then which of the following relations is a function from $\mathrm{A}$ to $B$?

1. $\left\{\right(1,2),(2,3),(3,4),(2,2\left)\right\}$

2. $\left\{\right(1,2),(2,3),(1,3\left)\right\}$

3. $\left\{\right(1,3),(2,3),(3,3\left)\right\}$

4. $\left\{\right(1,1),(2,3),(3,4\left)\right\}$

Q.

State whether the sets $E=\left\{x:xisaprimenumberlessthan10\right\}$ and $F=\left\{1,3,5,7,9\right\}$ are equal or not.

Q. Leo is organising a party in home. He has 12 glasses of cold drink. He wants to serve equal number of glasses to all his guests such that no glass of cold drink is left.

What is the range of the relation from set of number of glasses of cold drink to set of number of guests ?

1. $\{1,2,3,4,5,6\}$
2. $\{12,6,4,3,2,1\}$
3. $\{12,6,4\}$

Q. A relation defined as $R=$ {$(x,y),(2x,2y)$}.
Match the following.

1. Relation
2. Domain
3. Range

Q. What will be the range of given relation $A:\left\{\right(5,8),(3,-2),(1,4),(9,6\left)\right\}$

1. $\{8,-2,4,6\}$
2. $\{5,3,1,9\}$
3. $\{-2,5,4,6\}$
4. None of the above

Q. A student goes to play baseball 6 miles away from his home riding a bicycle. In $1^{st}$ mile 100 calories are spent. In $2^{nd}$ mile 300 calories are spent. For further miles, number of calories are spent in the arithmetic sequence.
What is the range of relation from set of distance covered to set of number of calories spent?

1. $\{100,300,500,700,900,1100\}$
2. $\{100,300,400,500,900,1100\}$
3. $\{100,300,500,700\}$

Q. A relation R is given as $R=\left\{\right(1,2),(5,6\left)\right\}$. Choose the correct pair from the following.

1. Ordered pairs
2. Domain
3. {$1,5$}
4. {$2,6$}
5. Range
6. $(1,2),(5,6)$

Q. Relation from a set of even natural numbers to a set of prime numbers is such that elements from both sets are equal.
Number of elements in domain of the relation is

Q. A relation P is defined as a set of ordered pairs $\left\{\right(-6,-2),(1,-1),(3,0),(5,1\left)\right\}$. What are the domain and Range of P ?

1. Domain : $\{-6,1,3,5\}$
   Range : $-3<Z<2$
2. Domain : $x\ge 0$
   Range : $\left(-2,-1,0,1\right\}$
3. Domain : $x\ge 2$
   Range : $-2\le Z\le 1$
4. All of the above.

Q. The set of values of '$y$' in the ordered pairs $(x,y)$ of a relation $R$ forms the domain of the relation $R$.

1. True
2. False

Q. A relation $R$ is given as $R=\left\{\right(1,8),(2,14),(3,17),(4,20\left)\right\}$ .The domain of this relation is

1. {$1,2,3,4$}
2. { $8,14,17,20$}
3. {$1,2,17,20$}

Q. $\{1,2,3,4\}$ is the domain of which of the relation $R$ given in the following options?

1. $R=\left\{\right(2,1),(3,4),(5,6),(7,8\left)\right\}$
2. $R=\left\{\right(1,1),(2,2),(3,3),(4,4\left)\right\}$
3. $R=\left\{\right(3,1),(5,2),(7,3),(9,4\left)\right\}$
4. $R=\left\{\right(1,1),(1,2),(1,3),(1,4\left)\right\}$