Consider a binary operation - on set 1-2-3-4-5 given by the following multiplication table-ii Is - commutative- -beginarray -c-c-c-c-c-c-Whelast - 1 - 2 - 3 - 4 - 5 Illhline1 - 1 - 1 - 1 - 1 - 1 lIVhline2 - 1 - 2 - 1 - 2 - 111 hline3 - 1 - 1 - 3 - 1 - 1 Whline4 - 1 - 2 - 1 - 4 - 1 lllhline5 - 1 - 1 - 1 - 1 - 5 111hline array

For every a,b ∈ 1,2,3,4,5,we have a × b =b × a. Therefore, the operation ∗ is commutative ...

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Standard XII

Mathematics

Commutative Law of Binary Operation

Consider a bi...

Question

Consider a binary operation $$ on set{1,2,3,4,5} given by the following multiplication table:
(ii) Is $$ commutative?

$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

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Solution

For every $a, b \in$ {1,2,3,4,5},we have $a \times b = b \times a$ .
Therefore, the operation $*$ is commutative

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Consider a binary operation $*$ on set{1,2,3,4,5} given by the following multiplication table:
(iii)Compute $(2 * 3) \times (4 * 5)$
$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

Consider a binary operation $*$ on set{1,2,3,4,5} given by the following multiplication table:
(i)Compute $(2 * 3) * 4$ and $2 * (3 * 4)$

$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

(ii) Is $*$ commutative?

$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

(iii)Compute $(2 * 3) \times (4 a s t 5)$
$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

Consider a binary operation * on the set {1, 2, 3, 4, 5} given by the following multiplication table.

(i) Compute (2 * 3) * 4 and 2 * (3 * 4)

(ii) Is * commutative?

(iii) Compute (2 * 3) * (4 * 5).

(Hint: use the following table)

*	1	2	3	4	5
1	1	1	1	1	1
2	1	2	1	2	1
3	1	1	3	1	1
4	1	2	1	4	1
5	1	1	1	1	5

$\begin{matrix} Components of Reflec Arc & Functions 1 & Receptor & a & Receives information from efferent nueron and shows appropriate response 2 & Afferent neron & b & Carries information from spinal cord to the effector organ 3 & Interneuron & c & Process information and Generates response 4 & Efferent Neuron & d & Receives information and generates impulses 5 & Effector & e & Carries information from receptor to inter neurons in the spinal cord \end{matrix}$

Q. Match the following based on cell shapes.

\begin{matrix} Column-I & Column-II A. & Round and biconcave & 1. & Nerve cell B. & Long and narrow & 2. & Leucocyte C. & Branched and long & 3. & Erythrocyte D. & Amoeboid & 4. & Tracheid E. & Elongated & 5. & Columnar epithelium \end{matrix}

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Consider a binary operation ∗ on set{1,2,3,4,5} given by the following multiplication table: (ii) Is ∗ commutative? ∗12345111111212121311311412141511115

For every a,b∈ {1,2,3,4,5},we have a×b=b×a. Therefore, the operation ∗ is commutative

Consider a binary operation $$ on set{1,2,3,4,5} given by the following multiplication table:
(ii) Is $$ commutative?

$\begin{matrix} * & 1 & 2 & 3 & 4 & 5 1 & 1 & 1 & 1 & 1 & 1 2 & 1 & 2 & 1 & 2 & 1 3 & 1 & 1 & 3 & 1 & 1 4 & 1 & 2 & 1 & 4 & 1 5 & 1 & 1 & 1 & 1 & 5 \end{matrix}$

For every $a, b \in$ {1,2,3,4,5},we have $a \times b = b \times a$ .
Therefore, the operation $*$ is commutative