Construct the cayley table for the binary operation * defined on the set S = 1 , 2 , 3 , 4 by the rule that a * b = a b m o d 5 for any a , b ∈ S . Using the pattern of the table. Show that the operation * is a commutative.

Given S = { 1 , 2 , 3 , 4 } and a * b = a b ( mod 5 ) ∀ a , b ∈ S . ⇒ 1 * 2 = 2 ( m o d 5 ) , 2 * 3 = 1 ( m o d 5 ) Multiply a & b then divide it by 5 and enter the value of the remainder in each box. * 1 2 3 4 1 1 2 3 4 2 2 4 1 3 3 3 1 4 2 4 4 3 2 1 Cayley table's values are symmetric along its diagonal axis. Hence, * is commutative.

Construct the cayley table for the binary operation * defined on the set S = 1 , 2 , 3 , 4 by the rule that a * b = a b m o d 5 for any a , b ∈ S . Using the pattern of the table. Show that the operation * is a commutative.

Given S = { 1 , 2 , 3 , 4 } and a * b = a b ( mod 5 ) ∀ a , b ∈ S . ⇒ 1 * 2 = 2 ( m o d 5 ) , 2 * 3 = 1 ( m o d 5 ) Multiply a & b then divide it by 5 and enter the value of the remainder in each box. * 1 2 3 4 1 1 2 3 4 2 2 4 1 3 3 3 1 4 2 4 4 3 2 1 Cayley table's values are symmetric along its diagonal axis. Hence, * is commutative.

* is a binary operation defined on the set A = 1 , 2 , 3 , 4 , 5 by a * b = min a , b for all a , b ∈ A . Form the cayley table or multiplication table for the operation * . Use the table to examine if * is commutative.

Given A = { 0 , 1 , 2 , 3 , 4 } and a * b = min a , b ∀ a , b ∈ A . ⇒ 1 * 2 = min 1 , 2 = 1 , 2 * 3 = min 2 , 3 = 2 and so on * 1 2 3 4 5 1 1 1 1 1 1 2 1 2 2 2 2 3 1 2 3 3 3 4 1 2 3 4 4 5 1 2 3 4 5 Cayley table's values are symmetric along its diagonal axis. Hence, * is commutative.

E M B I B E

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 15

EASY

12th West Bengal Board

IMPORTANT

Earn 100

Construct the cayley table for the binary operation $$ defined on the set $S = \{1, 2, 3, 4\}$ by the rule that $a b = a b$ $(m o d 5)$ for any $a, b \in S$ . Using the pattern of the table. Show that the operation $*$ is a commutative.

Important Questions on Relations and Functions

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 16

Form the cayley table for the binary operation $*$ defined on the set $S = \{0, 1, 2, 3, 4, 5\}$ by the rule that $a * b = (a + b) (m o d 6)$ and use the table to show that $*$ is commutative. Determine the identity element and $2^{- 1}$ with respect to $*$ $.$

EASY

12th West Bengal Board

IMPORTANT

RUDIMENTS of MATHEMATICS For Class 12 of +2 Level>Chapter 1 - Relations and Functions>EXERCISE>Q 17

$*$ is a binary operation defined on the set $A = \{1, 2, 3, 4, 5\}$ by $a * b$ $= \min \{a, b\}$ for all $a, b \in A$ . Form the cayley table or multiplication table for the operation $* .$ Use the table to examine if $*$ is commutative.