Relations and Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 1.4,Q.4, Page 25

Question

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)

$\begin{array}{c|ccccc} * & 1 & 2 & 3 & 4 & 5 \\ \hline 1 & 1 & 1 & 1 & 1 & 1 \\ 2 & 1 & 2 & 1 & 2 & 1 \\ 3 & 1 & 1 & 3 & 1 & 1 \\ 4 & 1 & 2 & 1 & 4 & 1 \\ 5 & 1 & 1 & 1 & 1 & 5 \end{array}$

Step-by-step Solution

(i) 2 $*$ 3 $=$ 1 and 3 $*$ 4 $=$ 1

Now, (2 $*$ 3) $*$ 4 $=$ 1 $*$ 4 $=$ 1 and 2 $*$ (3 $*$ 4) $=$ 2 $*$ 1 $=$ 1

(ii) 2 $*$ 3 $=$ 1 and 3 $*$ 2 $=$ 1 $\therefore$ 2 $*$ 3 $=$ 3 $*$ 2

Hence, the operation is commutative.

(iii) (2 $*$ 3) $*$ (4 $*$ 5) $=$ 1 $*$ 1 $=$ 1.

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