Consider a binary operation - on set 1-2-3-4-5 given by the following multiplication table-iiiCompute 2 - 3 -4 - 5Whelast - 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 lend array

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Standard XII

Mathematics

Equivalence Relation

Consider a bi...

Question

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

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Solution

We have $(2 * 3) = 1$ and $(4 * 5) = 1$
Therefore, $(2 * 3) * (4 * 5) = 1 * 1 = 1$

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

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

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

Find the mode from the given data.

1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2 , 3, 4, 1, 2, 3, 4, 1 ,2 , 3, 4, 5, 5, 1, 5, 5, 5, 3, 5, 1, 2, 4, 5, 6, 1, 2, 4, 2, 1

Q. The inverse of the matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 1 & 1 & 1 2 & 3 & 4 \end{matrix} ⎤ ⎥ ⎦

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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)×(4∗5) ∗12345111111212121311311412141511115

We have (2∗3)=1 and (4∗5)=1 Therefore, (2∗3)∗(4∗5)=1∗1=1

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

We have $(2 * 3) = 1$ and $(4 * 5) = 1$
Therefore, $(2 * 3) * (4 * 5) = 1 * 1 = 1$