Let A = { 1,2,3,4,...,10} and B = { 0,1,2,3,4}. The number of elements in the relation = {(a,b) in A X A : 2(a - b)^{2} + 3(a - b) in B} is .: Relation (Mathematics)

Exam (6$\ ^{th\ }$ April $1^{st\ }$ Shift 2023) 6th April Shift 1

Mathematics

Let

A = \{ 1,2,3,4,\ldots,10\}

and

B = \{ 0,1,2,3,4\}

. The number of elements in the relation

= \{(a,b) \in A \times A

2(a - b)^{2} + 3(a - b) \in B\}

\

(18):

A = \{ 1,2,3,4,\ldots\ldots,10\};B = \{ 0,1,2,3,4\}

R = \left\{ (a,b) \subset A \times A:2(a - b)^{2} + 3(a - b) \in B \right\}

Now,

2(a - b)^{2} + 3(a - b) = (a - b)|2(a - b) + 3| \in B

\Rightarrow a = b

a - b = - 2

\\ When,

a = b \Rightarrow 10

ordered pairs\\ When,

a - b = - 2 \Rightarrow 8

ordered pairs. Total

= 18

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