If A = { - 1 , 1 } . Find A × A × A

Given that, A = { - 1 , 1 } If it is known that for any non empty set A , A × A × A is defined as A × A × A = ( a , b , c ) : a , b , c ∈ A ∴ A × A × A = { ( - 1 , - 1 , - 1 ) , ( - 1 , - 1 , 1 ) , ( - 1 , 1 , - 1 ) , - 1 , 1 , 1 ( 1 , - 1 , - 1 ) , ( 1 , - 1 , 1 ) , ( 1 , 1 , - 1 ) , ( 1 , 1 , 1 ) }

Let R be a relation from Q to Q defined by R = { ( a , b ) : a , b ∈ Q and a - b ∈ Q } . Show that ( a , a ) ∈ R , for all a ∈ Q .

Given that: a , b ∈ Q and a - b ∈ Q To prove: ( a , a ) ∈ R ∀ a ∈ Q Since, a R a ⇒ a - a = 0 ∈ Q So, this will be reflexive relation or we can say ( a , a ) ∈ R ∀ a ∈ Q Hence Proved

Let R be a relation from Q to Q defined by R = { ( a , b ) : a , b ∈ Q and a - b ∈ Q } . Show that ( a , b ) ∈ R implies ( b , a ) ∈ R

We know that a relation R on a set A is called symmetric if ( b , a ) ∈ R holds when ( a , b ) ∈ R Given that, ( a , b ) ∈ R Since, a R b ⇒ a - b ∈ Q ⇒ - ( b - a ) ∈ Q Also, we can say b R a It is symmetric relation. Hence Proved

Let R be a relation from Q to Q defined by R = { ( a , b ) : a , b ∈ Q and a - b ∈ Q . Show that ( a , b ) ∈ R , ( b , c ) ∈ R implies ( a , c ) ∈ R

Given ( a , b ) ∈ R , ( b , c ) ∈ R Since, a R b ⇒ a - b ∈ Q Also b R c ⇒ b - c ∈ Q Thus ( a - b ) + ( b - c ) ∈ Q ⇒ ( a - c ) ∈ Q ⇒ a R c Hence, it is transitive or we can say ( a , c ) ∈ R

E M B I B E

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 10

MEDIUM

11th CBSE

IMPORTANT

Earn 100

Draw the graph $f (x) = x^{2}$

Important Questions on Relations and Functions

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 1

Let

A = {1, 2, 3, 4}, B = {3, 4, 5, 6, 7},

then what is the value of

n [(A \times B) \cap (B \times A)]

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 2

If the set

A

has

3

elements and the set

B = {3, 4, 5},

then find the number of elements in

(A \times B)

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 3

If

A = {- 1, 1}

. Find

A \times A \times A

MEDIUM

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 4

Let $f (x) = x^{2}$ and $g (x) = 2 x + 1$ be two real functions.

Find $(f + g) (x), (f - g) (x), (f g) (x)$ and $(\frac{f}{g}) (x)$ .

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 5

Let $R$ be a relation from $Q$ to $Q$ defined by $R = {(a, b) : a, b \in Q$ and $a - b \in Q}$ . Show that $(a, a) \in R,$ for all $a \in Q$ .

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 5

Let $R$ be a relation from $Q$ to $Q$ defined by $R = {(a, b) : a, b \in Q$ and $a - b \in Q}$ . Show that $(a, b) \in R$ implies $(b, a) \in R$

EASY

11th CBSE

IMPORTANT

Golden MATHEMATICS CLASS 11>Chapter 2 - Relations and Functions>SELF EVALUATION TEST>Q 5

Let $R$ be a relation from $Q$ to $Q$ defined by $R = {(a, b) : a, b \in Q$ and $a - b \in Q$ . Show that $(a, b) \in R, (b, c) \in R$ implies $(a, c) \in R$