Let A = \ 1,2,3,4\ and R be a relation on the set A x A defined by R = \((a,b),(c,d)):2a + 3b = 4c + 5d\. Then the number of elements in R is

(6) : A = \ 1,2,3,4\\ A x A = \(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3), (2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)\ R = \((a,b),(c,d)):2a + 3b = 4c + 5d\\ On checking the elements of A x A, we get \((1,4),(1,2)),((2,3),(2,1)),((3,1),(1,1)),((3,4), (2,2)),((4,2),(1,2)),((4,3),(3,1))\ will satisfy R.\ Therefore Number of elements in R is 6 .

Let A = { 1,2,3,4} and R be a relation on the set A ... | Relation (Mathematics)

Exam (15 $\ ^{th\ }$ April $1^{st\ }$ Shift 2023)

Mathematics

Let

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

and

R

be a relation on the set

A \times

A

defined by

R = \{((a,b),(c,d)):2a + 3b = 4c + 5d\}

. Then the number of elements in

R

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Explanation

(6) :

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

A \times A = \{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3)

(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)\}

R = \{((a,b),(c,d)):2a + 3b = 4c + 5d\}

\\ On checking the elements of

A \times A

, we get

\{((1,4),(1,2)),((2,3),(2,1)),((3,1),(1,1)),((3,4)

(2,2)),((4,2),(1,2)),((4,3),(3,1))\}

will satisfy

R

.\\

\therefore\

Number of elements in

R

is 6 .

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Explanation

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